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In this pdf, we will get to know about place values in numbers. Place value is the value of each digit in a number. For example, the 5 in 350 represents 5 tens, or 50; however, the 5 in 5,006 represents 5 thousands, or 5,000.

1.
**Please use the resources on this page to review and practice math concepts learned

throughout the year.**

**I highly recommend that you create a username and password for Learn Zillion. It is

free and there are video lessons to help with every math standard. I link to those videos

throughout this webpage.**

Place Value

Place Value Vocabulary

place value – the position of a value – what an individual digit digit – a symbol used to make a

digit in a number (ex. In 4.345, is worth in a number (ex. in numeral (ex. 8 is a digit that

the 5 is in the thousandths 4.345, the value of the 3 is makes up the number 568.) Just

place.) Place value is a word. 0.3, or 3/10.) Value is a number. as letters make words, digits

make numbers.

standard form – the most expanded form – writing a word form – A number

common way to write a number to show the value of written out in words (ex. 4.345

number (ex. 435,678) each digit (ex. 4.345 = (4 x 1) + = four and three hundred forty

(3 x 0.1) + (4 x 0.01) + (5 x five thousandths)

0.001))

model – showing a number using decimal – a point between a compare – tell whether a

base ten blocks, number lines, or whole number and a decimal number is greater than, less

another method. fraction than, or equal to another

number

tenths – one part in ten equal hundredths – one part in one thousandths – one part in one

parts (ex. 1/10, 0.1) hundred equal parts (ex. 1/100, thousand equal parts (ex.

0.01) 1/1000, 0.001)

greater than - > (ex. 5.5 is less than - < (ex. 5.4 is less than equal to – = (ex. 5.50 is equal

greater than 5.4; 5.5 > 5.4) 5.5; 5.4 < 5.5) to 5.5; 5.50 = 5.5)

Decimal Place Value (position) and Value (worth)

Ones Decimal (and) tenths hundredths thousandths

4 3 2 5

throughout the year.**

**I highly recommend that you create a username and password for Learn Zillion. It is

free and there are video lessons to help with every math standard. I link to those videos

throughout this webpage.**

Place Value

Place Value Vocabulary

place value – the position of a value – what an individual digit digit – a symbol used to make a

digit in a number (ex. In 4.345, is worth in a number (ex. in numeral (ex. 8 is a digit that

the 5 is in the thousandths 4.345, the value of the 3 is makes up the number 568.) Just

place.) Place value is a word. 0.3, or 3/10.) Value is a number. as letters make words, digits

make numbers.

standard form – the most expanded form – writing a word form – A number

common way to write a number to show the value of written out in words (ex. 4.345

number (ex. 435,678) each digit (ex. 4.345 = (4 x 1) + = four and three hundred forty

(3 x 0.1) + (4 x 0.01) + (5 x five thousandths)

0.001))

model – showing a number using decimal – a point between a compare – tell whether a

base ten blocks, number lines, or whole number and a decimal number is greater than, less

another method. fraction than, or equal to another

number

tenths – one part in ten equal hundredths – one part in one thousandths – one part in one

parts (ex. 1/10, 0.1) hundred equal parts (ex. 1/100, thousand equal parts (ex.

0.01) 1/1000, 0.001)

greater than - > (ex. 5.5 is less than - < (ex. 5.4 is less than equal to – = (ex. 5.50 is equal

greater than 5.4; 5.5 > 5.4) 5.5; 5.4 < 5.5) to 5.5; 5.50 = 5.5)

Decimal Place Value (position) and Value (worth)

Ones Decimal (and) tenths hundredths thousandths

4 3 2 5

2.
The 4 is in the ones place. The value of the 4 is 4

The 3 is in the tenths place. The value of the 3 is 0.3

The 2 is in the hundredths place. The value of the 2 is 0.02

The 5 is in the thousandths place. The value of the 5 is 0.005

Video Lesson for place value of decimals:

http://studyjams.scholastic.com/studyjams/jams/math/decimals-

percents/place-value-decimals.htm

Game to practice decimal place value:

Paper Boy Place Value:

http://www.sheppardsoftware.com/mathgames/decimals/scooter

QuestDecimal.htm

Pirate Place Value:

http://mrnussbaum.com/placevaluepirates1/

Video Lesson for reading decimals:

https://learnzillion.com/lessons/428-name-decimals-through-the-

thousandths-place

Game for practice with reading decimals:

Decimals of the Caribbean: http://mrnussbaum.com/docrb1/

Standard form, word form, and expanded form:

Standard Expanded Form Word Form

0.034 (3 x 0.01) + (4 x 0.001) Thirty-four thousandths

5.67 (5 x 1) + (6 x 0.1) + (7 x 0.01) Five and sixty-seven

hundredths

The 3 is in the tenths place. The value of the 3 is 0.3

The 2 is in the hundredths place. The value of the 2 is 0.02

The 5 is in the thousandths place. The value of the 5 is 0.005

Video Lesson for place value of decimals:

http://studyjams.scholastic.com/studyjams/jams/math/decimals-

percents/place-value-decimals.htm

Game to practice decimal place value:

Paper Boy Place Value:

http://www.sheppardsoftware.com/mathgames/decimals/scooter

QuestDecimal.htm

Pirate Place Value:

http://mrnussbaum.com/placevaluepirates1/

Video Lesson for reading decimals:

https://learnzillion.com/lessons/428-name-decimals-through-the-

thousandths-place

Game for practice with reading decimals:

Decimals of the Caribbean: http://mrnussbaum.com/docrb1/

Standard form, word form, and expanded form:

Standard Expanded Form Word Form

0.034 (3 x 0.01) + (4 x 0.001) Thirty-four thousandths

5.67 (5 x 1) + (6 x 0.1) + (7 x 0.01) Five and sixty-seven

hundredths

3.
8.9 (8 x 1) + (9 x 0.1) Eight and nine tenths

Writing Decimals in standard form: Standard form is the common way

we write numbers. For example, five and twenty-three hundredths is

5.23 in standard form.

Writing Decimals in Expanded Form: In the past grades, expanded form

has been simpler. For 456, you would write 400 + 50 + 6. In fifth

grade, the complexity of expanded form changes. Each written value is

broken down even further, adding in a multiplication component.

Now, 456 would look like this: (4 x 100) + (5 x 10) + (6 x 1)

Let’s look at a decimal number in 5th grade expanded form. For

instance, 4.567 in expanded form could look like this:

(4 x 1) + (5 x 0.1) + (6 x 0.01) + (7 x 0.001)

or this: (4 x 1) + (5 x ) + (6 x ) + (7 x )

Video Lesson for expanded form:

https://learnzillion.com/lessons/429-write-decimals-in-expanded-

notation

Writing Decimals in Word Form: When you write a decimal number in

word form you simply read the decimal and write what you say. For

example, if I see the decimal 5.673, I would read the decimal to myself,

remembering that I say “and” when I come to the decimal point, and

write what I say. 5.673 in word form would be five and six hundred

seventy-three thousandths.

Writing Decimals in standard form: Standard form is the common way

we write numbers. For example, five and twenty-three hundredths is

5.23 in standard form.

Writing Decimals in Expanded Form: In the past grades, expanded form

has been simpler. For 456, you would write 400 + 50 + 6. In fifth

grade, the complexity of expanded form changes. Each written value is

broken down even further, adding in a multiplication component.

Now, 456 would look like this: (4 x 100) + (5 x 10) + (6 x 1)

Let’s look at a decimal number in 5th grade expanded form. For

instance, 4.567 in expanded form could look like this:

(4 x 1) + (5 x 0.1) + (6 x 0.01) + (7 x 0.001)

or this: (4 x 1) + (5 x ) + (6 x ) + (7 x )

Video Lesson for expanded form:

https://learnzillion.com/lessons/429-write-decimals-in-expanded-

notation

Writing Decimals in Word Form: When you write a decimal number in

word form you simply read the decimal and write what you say. For

example, if I see the decimal 5.673, I would read the decimal to myself,

remembering that I say “and” when I come to the decimal point, and

write what I say. 5.673 in word form would be five and six hundred

seventy-three thousandths.

4.
Modeling Decimals with Base-ten Blocks: You can model decimals using

base-ten blocks. Here is how:

If we are modeling a decimal that only goes to the tenths or

hundredths place (ex. 4.5 or 4.56), we can use the hundreds block

(“flat”), the tens rod (“long”), and the ones cubes.

Flat: Long: Small Cubes:

1 whole 1 tenth 1 hundredth

1 0.1 or 1/10 0.01 0r 1/100

1.24

3.6

0.75

If we are modeling a decimal that goes to the thousandths place, the

base ten blocks would represent different values. To represent one

whole, we would use the large cube as one whole, the “flat” as one

tenth, the “long” as one hundredth, and the small cube as one

base-ten blocks. Here is how:

If we are modeling a decimal that only goes to the tenths or

hundredths place (ex. 4.5 or 4.56), we can use the hundreds block

(“flat”), the tens rod (“long”), and the ones cubes.

Flat: Long: Small Cubes:

1 whole 1 tenth 1 hundredth

1 0.1 or 1/10 0.01 0r 1/100

1.24

3.6

0.75

If we are modeling a decimal that goes to the thousandths place, the

base ten blocks would represent different values. To represent one

whole, we would use the large cube as one whole, the “flat” as one

tenth, the “long” as one hundredth, and the small cube as one

5.
Large Cube: Flat: Long: Small Cube:

1 whole 1 tenth 1 hundredth

1 0.1 or 1/10 0.01 or 1/100 1 thousandth

0.001 or 1/1000

2.456

0.870

1.003

Video Lesson for Decimal Models:

https://learnzillion.com/lessons/3776-read-and-write-decimals-

using-base-ten-blocks

Games/Practice for practicing decimal models:

o Decimals to Tenths Place:

http://www.sheppardsoftware.com/mathgames/decimals/D

ecimalModels10.htm

o Decimals to Hundredths Place:

http://www.sheppardsoftware.com/mathgames/decimals/D

ecimalModels.htm

o Decimals to Thousandths Place:

1 whole 1 tenth 1 hundredth

1 0.1 or 1/10 0.01 or 1/100 1 thousandth

0.001 or 1/1000

2.456

0.870

1.003

Video Lesson for Decimal Models:

https://learnzillion.com/lessons/3776-read-and-write-decimals-

using-base-ten-blocks

Games/Practice for practicing decimal models:

o Decimals to Tenths Place:

http://www.sheppardsoftware.com/mathgames/decimals/D

ecimalModels10.htm

o Decimals to Hundredths Place:

http://www.sheppardsoftware.com/mathgames/decimals/D

ecimalModels.htm

o Decimals to Thousandths Place:

6.
Model the following decimals using base ten blocks on paper:

6.678

1.340

2.522

Showing Decimals on a Number Line: Decimals can be placed on a

number line just like whole numbers. For example, 1.5 would fall here on

the number line:

1 1.5 2

1.55 would fall here:

Video lesson for placing decimals on a number line:

http://studyjams.scholastic.com/studyjams/jams/math/decimals-

percents/place-decimal-number-line.htm

Game for placing decimals on number line:

http://www.sheppardsoftware.com/mathgames/decimals/mathm

an_decimal_numberline.htm

Comparing Decimals:

You can compare two decimals using the symbols > (greater than), <

(less than), and = (equal to). There are several ways to compare

6.678

1.340

2.522

Showing Decimals on a Number Line: Decimals can be placed on a

number line just like whole numbers. For example, 1.5 would fall here on

the number line:

1 1.5 2

1.55 would fall here:

Video lesson for placing decimals on a number line:

http://studyjams.scholastic.com/studyjams/jams/math/decimals-

percents/place-decimal-number-line.htm

Game for placing decimals on number line:

http://www.sheppardsoftware.com/mathgames/decimals/mathm

an_decimal_numberline.htm

Comparing Decimals:

You can compare two decimals using the symbols > (greater than), <

(less than), and = (equal to). There are several ways to compare

7.
1. Compare decimals using fractions: When we read decimals, what we

say sounds like a fraction. For example, 0.3 is three tenths, or 3/10. If

we convert both decimals we are comparing to fractions, we can easily

compare them.

For example: Compare: 0.9 > 0.8

Video Lesson for Comparing Decimals using Fractions:

https://learnzillion.com/lessons/562-compare-decimals-using-

fractions

Practice for Comparing Decimals using fractions:

o Compare the following:

1.19 1.11

0.344 0.034

2. Comparing Decimals Using a Number Line: We can also compare

decimals by placing them on a number line and visually comparing their

positions. Watch the following video lesson to see how.

Comparing Decimals Using a Number Line Video Lesson:

https://learnzillion.com/lessons/563-compare-decimals-using-a-

number-line

3. Comparing Decimals Using Base ten Blocks: We can also compare

decimals by looking at the models we create with base ten blocks. For

example, let’s compare 0.04 and 0.045 using models.

0.04 < 0.045

say sounds like a fraction. For example, 0.3 is three tenths, or 3/10. If

we convert both decimals we are comparing to fractions, we can easily

compare them.

For example: Compare: 0.9 > 0.8

Video Lesson for Comparing Decimals using Fractions:

https://learnzillion.com/lessons/562-compare-decimals-using-

fractions

Practice for Comparing Decimals using fractions:

o Compare the following:

1.19 1.11

0.344 0.034

2. Comparing Decimals Using a Number Line: We can also compare

decimals by placing them on a number line and visually comparing their

positions. Watch the following video lesson to see how.

Comparing Decimals Using a Number Line Video Lesson:

https://learnzillion.com/lessons/563-compare-decimals-using-a-

number-line

3. Comparing Decimals Using Base ten Blocks: We can also compare

decimals by looking at the models we create with base ten blocks. For

example, let’s compare 0.04 and 0.045 using models.

0.04 < 0.045

8.
<

Video Lesson for Comparing Decimals with Models:

https://learnzillion.com/lessons/564-compare-decimals-using-base-

ten-blocks

4. Tricks for quickly comparing decimals: Now that you have an

understanding of the strategies you can use to compare decimals, here

are some quick ways:

“Balancing out” the numbers – It can look difficult when having

to compare decimals that go to different place values. For

example, you might be asked to compare 1.45 and 1.451. To easily

compare these decimals, you can make them look similar by adding

a zero to the end of the decimal with fewer places.

1.450 < 1.451

Adding a zero will not change the value of the decimal

because 45/100 is the same amount as 450/1000.

Now both decimals look similar, and you can easily tell

that four hundred fifty thousandths is less than four

hundred fifty-one thousandths.

“Cross-out Method” – this method can be useful when comparing

decimals or whole numbers. In this method, you examine each

place value carefully and cross out the place values that match

from left to right. For example, let’s compare 0.009 and 0.09.

0.009 < 0.09

Video Lesson for Comparing Decimals with Models:

https://learnzillion.com/lessons/564-compare-decimals-using-base-

ten-blocks

4. Tricks for quickly comparing decimals: Now that you have an

understanding of the strategies you can use to compare decimals, here

are some quick ways:

“Balancing out” the numbers – It can look difficult when having

to compare decimals that go to different place values. For

example, you might be asked to compare 1.45 and 1.451. To easily

compare these decimals, you can make them look similar by adding

a zero to the end of the decimal with fewer places.

1.450 < 1.451

Adding a zero will not change the value of the decimal

because 45/100 is the same amount as 450/1000.

Now both decimals look similar, and you can easily tell

that four hundred fifty thousandths is less than four

hundred fifty-one thousandths.

“Cross-out Method” – this method can be useful when comparing

decimals or whole numbers. In this method, you examine each

place value carefully and cross out the place values that match

from left to right. For example, let’s compare 0.009 and 0.09.

0.009 < 0.09

9.
If we cross out the matching place values first, we would cross out the

ones place on both numbers because they are both zero, and the tens

place on both numbers because they are both zero. Now we are looking

at a zero in the hundredths place of the first number, and a nine in

the hundredths place of the second number. Since zero hundredths is

less than nine hundredths, 0.009 is less than 0.09.

Game for Comparing Decimals:

http://www.sheppardsoftware.com/mathgames/decimals/Compa

reDecimals.htm

Ordering Decimals:

Once you have learned how to compare decimals, you can put them in

order from least to greatest or from greatest to least as well. Watch

the following videos to see how to order decimals:

https://learnzillion.com/lessons/34-compare-and-order-simple-

decimals

https://learnzillion.com/lessons/35-compare-and-order-decimals-

to-the-thousandths-place

Rounding Decimals to Any Place:

You may be asked to round a decimal number to the nearest whole

number, to the nearest tenth, to the nearest hundredth, or to the

nearest thousandth.

You can round decimal numbers by using a number line.

Click on the following links to see how to round decimals using a number

ones place on both numbers because they are both zero, and the tens

place on both numbers because they are both zero. Now we are looking

at a zero in the hundredths place of the first number, and a nine in

the hundredths place of the second number. Since zero hundredths is

less than nine hundredths, 0.009 is less than 0.09.

Game for Comparing Decimals:

http://www.sheppardsoftware.com/mathgames/decimals/Compa

reDecimals.htm

Ordering Decimals:

Once you have learned how to compare decimals, you can put them in

order from least to greatest or from greatest to least as well. Watch

the following videos to see how to order decimals:

https://learnzillion.com/lessons/34-compare-and-order-simple-

decimals

https://learnzillion.com/lessons/35-compare-and-order-decimals-

to-the-thousandths-place

Rounding Decimals to Any Place:

You may be asked to round a decimal number to the nearest whole

number, to the nearest tenth, to the nearest hundredth, or to the

nearest thousandth.

You can round decimal numbers by using a number line.

Click on the following links to see how to round decimals using a number

10.
Round decimals to the nearest whole number:

https://learnzillion.com/lessons/3430-round-decimals-to-the-

nearest-whole-number

Round decimals to the nearest tenth:

https://learnzillion.com/lessons/3432-round-decimals-to-the-

nearest-tenth

Round decimals to the nearest hundredth:

https://learnzillion.com/lessons/3322-round-decimals-to-the-

nearest-hundredth

Round decimals to the nearest thousandth, or any other place:

https://learnzillion.com/lessons/3522-round-decimals-to-any-place

You may also use another strategy to round decimals. For example, let’s

round 3.456 to the nearest tenth.

Step one: Underline the place you are rounding to 3.456

Step two: Circle the place to the right of the underlined place 3.456

Step three: If the circled number is 4 or less, then the underlined

number stays the same. If the circled number is 5 or more, then the

underlined number increases by one. 3.456

Step four: The numbers to the right of the underlined number change

to zeros, and the numbers to the left of the underlined number stay

the same. Answer: 3.500 or 3.5

Games for Rounding Decimals:

http://www.sheppardsoftware.com/mathgames/decimals/scooter

QuestDecRound.htm

https://learnzillion.com/lessons/3430-round-decimals-to-the-

nearest-whole-number

Round decimals to the nearest tenth:

https://learnzillion.com/lessons/3432-round-decimals-to-the-

nearest-tenth

Round decimals to the nearest hundredth:

https://learnzillion.com/lessons/3322-round-decimals-to-the-

nearest-hundredth

Round decimals to the nearest thousandth, or any other place:

https://learnzillion.com/lessons/3522-round-decimals-to-any-place

You may also use another strategy to round decimals. For example, let’s

round 3.456 to the nearest tenth.

Step one: Underline the place you are rounding to 3.456

Step two: Circle the place to the right of the underlined place 3.456

Step three: If the circled number is 4 or less, then the underlined

number stays the same. If the circled number is 5 or more, then the

underlined number increases by one. 3.456

Step four: The numbers to the right of the underlined number change

to zeros, and the numbers to the left of the underlined number stay

the same. Answer: 3.500 or 3.5

Games for Rounding Decimals:

http://www.sheppardsoftware.com/mathgames/decimals/scooter

QuestDecRound.htm

11.
http://www.math-play.com/rounding-decimals-game-1/rounding-

decimals-game.html

Place Value Relationships

Place value relationships refers to the relationship between each place

value in a number.

In the number 8,888 the 8 in the tens place is worth 10 times the 8

in the ones place. The 8 in the hundreds place is worth 100 times the

ones place. The 8 in the thousands place is worth 1,000 times the ones

decimals-game.html

Place Value Relationships

Place value relationships refers to the relationship between each place

value in a number.

In the number 8,888 the 8 in the tens place is worth 10 times the 8

in the ones place. The 8 in the hundreds place is worth 100 times the

ones place. The 8 in the thousands place is worth 1,000 times the ones

12.
Going the other way, the 8 in the ones place is worth

of the tens place

of the hundreds place

of the thousands place

Students need to be able to write statements comparing numbers in

different place values. For example, they might be asked to compare

the value of the 8 in 3.89 to the value of the 8 in 8.39. To compare

the values of the numbers, you must first determine the value. The

value of the 8 in 3.89 is 0.8. The value of the 8 in 8.39 is 8.

Therefore, the value of the 8 in 3.89 is the value or 10 times

smaller than) of the 8 in 8.39.

Videos for Comparing Place Values:

https://learnzillion.com/lessons/2676-recognize-place-value-

relationships-by-multiplying-and-dividing-by-ten

https://learnzillion.com/lessons/3363-compare-the-value-of-the-

digits-in-a-decimal-number

Games for Comparing Place Values:

http://www.ixl.com/math/grade-5/convert-between-place-

values

http://www.sheppardsoftware.com/mathgames/placevalue/Place

ValuesShapesShoot.htm

of the tens place

of the hundreds place

of the thousands place

Students need to be able to write statements comparing numbers in

different place values. For example, they might be asked to compare

the value of the 8 in 3.89 to the value of the 8 in 8.39. To compare

the values of the numbers, you must first determine the value. The

value of the 8 in 3.89 is 0.8. The value of the 8 in 8.39 is 8.

Therefore, the value of the 8 in 3.89 is the value or 10 times

smaller than) of the 8 in 8.39.

Videos for Comparing Place Values:

https://learnzillion.com/lessons/2676-recognize-place-value-

relationships-by-multiplying-and-dividing-by-ten

https://learnzillion.com/lessons/3363-compare-the-value-of-the-

digits-in-a-decimal-number

Games for Comparing Place Values:

http://www.ixl.com/math/grade-5/convert-between-place-

values

http://www.sheppardsoftware.com/mathgames/placevalue/Place

ValuesShapesShoot.htm

13.
Exponents

Note: Any number with an exponent of zero is equal to one

(ex. =1)

In fifth grade, we discover the meaning of exponents, then set our

focus on powers of ten

Powers of Ten

Here are several videos to explain powers of ten.

Explain Patterns in Zeros When Multiplying by Powers of Ten

Represent Powers of Ten Using Exponents

Explain Patterns in the Placement of the Decimal Point When

Multiplying by Powers of Ten

Explain Patterns in the Placement of the Decimal Point When Dividing

by Powers of Ten

In the past, students have learned that when multiplying by powers of

ten (10, 100, 1,000, etc.) The amount of zeros in the power of ten

Note: Any number with an exponent of zero is equal to one

(ex. =1)

In fifth grade, we discover the meaning of exponents, then set our

focus on powers of ten

Powers of Ten

Here are several videos to explain powers of ten.

Explain Patterns in Zeros When Multiplying by Powers of Ten

Represent Powers of Ten Using Exponents

Explain Patterns in the Placement of the Decimal Point When

Multiplying by Powers of Ten

Explain Patterns in the Placement of the Decimal Point When Dividing

by Powers of Ten

In the past, students have learned that when multiplying by powers of

ten (10, 100, 1,000, etc.) The amount of zeros in the power of ten

14.
are added to the original number. For example, when multiplying 23 x

10, you would just add a zero to 23, making the product 230. When

multiplying 23 x 100, you would add two zeros, making the product

What is actually happening is that the decimal is moving. When you

multiply 23 x 10, the decimal is moving one place to the right. When

you multiply by 100, the decimal is moving two places to the right.

23 x 10 = 23.0. = 230 23 x 100 = 23.00. = 2,300

Here is how these problems look with the 10 and 1,000 in exponential

23 x = 230 23 x = 2,300

When dividing by powers of ten, the decimal shifts to the left rather

than to the right, because when you divide, the number gets smaller

23 ÷ 10 = 2.3. = 2.3 23 ÷ 100 = .23. = .23

23 ÷ = 2.3. = 2.3 23 ÷ = .23. = .23

Another important concept to understand is that multiplying by a

decimal is similar to dividing. Here are a few handy charts to sum up

how the decimal moves with different operations.

10, you would just add a zero to 23, making the product 230. When

multiplying 23 x 100, you would add two zeros, making the product

What is actually happening is that the decimal is moving. When you

multiply 23 x 10, the decimal is moving one place to the right. When

you multiply by 100, the decimal is moving two places to the right.

23 x 10 = 23.0. = 230 23 x 100 = 23.00. = 2,300

Here is how these problems look with the 10 and 1,000 in exponential

23 x = 230 23 x = 2,300

When dividing by powers of ten, the decimal shifts to the left rather

than to the right, because when you divide, the number gets smaller

23 ÷ 10 = 2.3. = 2.3 23 ÷ 100 = .23. = .23

23 ÷ = 2.3. = 2.3 23 ÷ = .23. = .23

Another important concept to understand is that multiplying by a

decimal is similar to dividing. Here are a few handy charts to sum up

how the decimal moves with different operations.

15.
To multiply a number by a power of ten, you can use the exponent to

determine how the position of the decimal point changes in the product.

Problem Exponent Move decimal point:

0 0 places to the right

1 1 place to the right

2 2 places to the right

3 3 place to the right

You can use place-value patterns to find the product of a number and

the decimals 0.1, 0.01, and so on.

Problem Multiply by: Move decimal point:

1 x 2,457 = 2,457 1 0 places to the left

0.1 x 2,457 = 245.7 0.1 1 place to the left

0.01 x 2,457 = 24.57 0.01 2 places to the left

To divide an number by 10, 100, or 1,000, use the number of zeros in

the divisor to determine how the position of the decimal point changes

in the quotient.

Problem Number of zeros: Move decimal point:

147 ÷1 = 147 0 0 places to the left

147 ÷10 = 147 1 1 place to the left

147 ÷100 = 147 2 2 places to the left

147 ÷1,000 = 147 3 3 places to the left

determine how the position of the decimal point changes in the product.

Problem Exponent Move decimal point:

0 0 places to the right

1 1 place to the right

2 2 places to the right

3 3 place to the right

You can use place-value patterns to find the product of a number and

the decimals 0.1, 0.01, and so on.

Problem Multiply by: Move decimal point:

1 x 2,457 = 2,457 1 0 places to the left

0.1 x 2,457 = 245.7 0.1 1 place to the left

0.01 x 2,457 = 24.57 0.01 2 places to the left

To divide an number by 10, 100, or 1,000, use the number of zeros in

the divisor to determine how the position of the decimal point changes

in the quotient.

Problem Number of zeros: Move decimal point:

147 ÷1 = 147 0 0 places to the left

147 ÷10 = 147 1 1 place to the left

147 ÷100 = 147 2 2 places to the left

147 ÷1,000 = 147 3 3 places to the left

16.
To divide a number by a power of ten, you can use the exponent to

determine how the position of the decimal point changes in the

Problem Exponent Move decimal point:

0 0 places to the left

1 1 place to the left

2 2 places to the left

Adding Decimals

Volume

Volume Vocabulary

volume – the amount of 3- measurement – finding a attribute – a characteristic of

demensional space an object number that shows the size or an object

occupies amount of something

solid figure – a 3-demensional right rectangular prism - a unit – a quantity used as a

object (ex. cube, pyramid, prism in which the angles standard measurement

rectangular prism, sphere, between the base and sides are

cylinder, etc.) right angles.

unit cube – a cube whose sides gap – a space or opening overlap – to cover part of the

are one unit long edge of something

cubic units – a unit to measure edge length – the length of an height – a measure of how tall

volume edge of a solid figure something is

area of base – the area of a multiplication – repeatedly adding addition – combining numbers to

solid figure’s base (L x W) numbers to find a product find the total

By the end of this unit, students should be able to recognize volume as an attribute of solid figures

and measure the volume of right rectangular prisms using unit cubes and the formula for volume.

Videos to help explain concepts of volume:

determine how the position of the decimal point changes in the

Problem Exponent Move decimal point:

0 0 places to the left

1 1 place to the left

2 2 places to the left

Adding Decimals

Volume

Volume Vocabulary

volume – the amount of 3- measurement – finding a attribute – a characteristic of

demensional space an object number that shows the size or an object

occupies amount of something

solid figure – a 3-demensional right rectangular prism - a unit – a quantity used as a

object (ex. cube, pyramid, prism in which the angles standard measurement

rectangular prism, sphere, between the base and sides are

cylinder, etc.) right angles.

unit cube – a cube whose sides gap – a space or opening overlap – to cover part of the

are one unit long edge of something

cubic units – a unit to measure edge length – the length of an height – a measure of how tall

volume edge of a solid figure something is

area of base – the area of a multiplication – repeatedly adding addition – combining numbers to

solid figure’s base (L x W) numbers to find a product find the total

By the end of this unit, students should be able to recognize volume as an attribute of solid figures

and measure the volume of right rectangular prisms using unit cubes and the formula for volume.

Videos to help explain concepts of volume:

17.
Identifying the parts of 3D figures

Difference between a square unit and a cubic unit

Understanding volume

Finding volume by counting cubes

Finding volume by multiplying the area of the base by the height

Finding volume using the formula length x width x height (L x W x H)

Finding edge lengths that aren’t labeled

Decomposing irregular 3D figures to find the volume

Games/Activities to practice concepts of volume:

Measuring volume by counting cubic units

Finding the volume of rectangular prisms (practice sheets)

Difference between a square unit and a cubic unit

Understanding volume

Finding volume by counting cubes

Finding volume by multiplying the area of the base by the height

Finding volume using the formula length x width x height (L x W x H)

Finding edge lengths that aren’t labeled

Decomposing irregular 3D figures to find the volume

Games/Activities to practice concepts of volume:

Measuring volume by counting cubic units

Finding the volume of rectangular prisms (practice sheets)