Introduction to Decimal Place Values

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Place Values in Decimals. The first digit after the decimal represents the tenths place. The next digit after the decimal represents the hundredths place. The remaining digits continue to fill in the place values until there are no digits left.
1. A Guide to Understanding
rd th
3 -4 Grade Math
Hundred Ten Thousands Hundreds Tens Ones . Ones Tenths Hundredths
Thousands Thousands
Place Value
2. Writing Whole Numbers
 Place value tells you how much each digit stands for.
 Use a hyphen when you use words to write 2-digit numbers
greater than 20 that have a digit other than zero in the ones place.
Example: Write 57 in words.
Answer: fifty-seven
Example: Write 80 in words.
Answer: eighty
 A place-value chart tells you how many hundreds, tens, & ones to
Example: A supermarket has 258 boxes of cereal on its shelves.
Hundreds Tens Ones
2 5 8
Or use a base ten model:
2 hundred 5 tens 8 ones
 Zeros may stand for nothing, but that doesn’t mean you can leave
them out. They keep other digits in the correct places.
Thousands Hundreds Tens Ones
1 0 3 0
Think: 1 thousand + 0 hundred + 3 tens + 0 ones
Write: 1,030
Say: One thousand thirty
3. Place Value Through the Millions
Millions Period Thousands Period Ones Period
Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones
9 1 4 0 2 6 0 0
The digits in large numbers are in groups of three places. The groups
are called periods. Commas are usually used to separate the periods.
Write: 91,402,600
Example: What is the value of the digit 4 in 91,402,600?
Answer: the digit 4 is in the hundred thousands place. Its value is 4
hundred thousand or 400,000.
Reading Large Numbers
Reading large numbers is easier than it looks. You only need to know
 How to read 3-digit numbers, and
 The names of the periods.
Example: How do you read 2,469,600?
1. Start at the left. Read the first comma. Say the name of the
period.two million
2. Read to the 2nd comma. Say the name of the next period.four
hundred sixty-nine thousand.
3. Read the three-digit number in the ones period. six hundred
 You don’t say the name of the ones period.
Answer: Say: two million, four hundred sixty-nine thousand, six
4. “AND” is for Decimals – Not Whole Numbers
When you read a whole number, don’t say the word and. Use and only
when you read a decimal point.
Write: 905 Write: 900.5
Say: nine hundred five Say: nine hundred and five tenths
(not nine hundred and five)
Comparing Whole Numbers
1. Line up the place values by lining up the ones.
2. Begin with the greatest place. Find the first place where the digits are
different. 563
 different
3. Compare the value of the digits in that place.
60 is greater than 20
So, 563>521
 BE careful when you compare numbers that don’t have the same
number of digits. Make sure you line up the ones places.
Suppose you want to compare 1246 and 896.
Lined up correctly at the ones place Lined up incorrectly
1246 1246
896 896
* When one whole number has more digits than another, it is greater.
So, 1246> 896 (the hungry alligator always eats the
bigger portion, the mouth of the symbol is open to the greater number)
5. Ordering Whole Numbers
It is easier to work with a group of numbers it they are in order: Order
can be from greatest to least, or from least to greatest.
If you know how to compare numbers, you know how to put a group of
numbers in order.
1. Line up the numbers at the ones place. 1127
2. Begin to compare at the greatest place. 841 is the least because it has
the fewest digits.
3. Compare the remaining numbers. Find the first place where the
digits are different. 1127
 different
Answer: The order from least to greatest is 841, 1127,1483
6. Money
U. S. coins and bills are based on ones, fives, and tens, which make them
easy to count. The dollar is the basic unit.
Penny Nickel Dine Quarter Half dollar
1¢ 5¢ 10¢ 25¢ 50¢
$0.01 $0.05 $0.10 $0.25 $0.50
$1 bill $5 bill $10 bill $20 bill
$1.00 $5.00 $10.00 $20.00
Write: 25¢ or $0.25 Write: $5.00
Say: twenty-five cents Say: five dollars
 Frank has $9.24
 Write $9.24
 Say: nine dollars and twenty-four cents (remember to say “and”
when you read the decimal point)
*$ and ¢ do not go together
Don’t write $ when you mean ¢, and don’t write¢ when you mean $
Correct Not Correct
47¢ $0.47¢
or or
$0.47 0.47¢