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In this pdf, we will be Multiplying and Dividing Decimals by 10, 100 and 1000.

1.
Multiplying and Dividing Decimals by 10, 100 and

1000.

Hopefully you are now feeling more confident when working with decimal numbers. We are now moving on to

looking at what happens when we multiply or divide a decimal number by 10, 100 or 1000. You might remember

doing this with whole numbers at the start of the year. A place value grid can really help complete these

calculations. You could make your own, or there are lots that you can download on the internet.

Multiplying Decimal Numbers by 10, 100 and 1000

When we multiply by 10, the

number gets 10 times bigger.

Therefore, the number moves one

place to the left on our place

value grid.

When we multiply by 100, the

number gets 100 times bigger.

Therefore, the number moves two

places to the left on our place

value grid.

When we multiply by 1000, the

number gets 1000 times bigger.

Therefore, the number moves

three places to the left on our

place value grid.

Example:

If I multiply 3.24 by 10, all my

counters will move one place to

the left.

My ones will move to the tens,

my tenths will move to the ones,

and my hundredths will move to

the tenths.

3.24 x 10 = 32.4

If I multiply 3.24 by 100, all my counters will move 2 places to

the left. If I multiply 3.24 by 1000, all my

counters will move three places to the

My ones will move to the hundreds, my tenths will move to

left.

the tens and my hundredths will move to the ones.

Can you work out what the answer will

3.24 x 100 = 324

be?

(if you don’t have any decimal values left, you do not have to Do you need to use any place value

include a decimal point in your answer) holders?

1000.

Hopefully you are now feeling more confident when working with decimal numbers. We are now moving on to

looking at what happens when we multiply or divide a decimal number by 10, 100 or 1000. You might remember

doing this with whole numbers at the start of the year. A place value grid can really help complete these

calculations. You could make your own, or there are lots that you can download on the internet.

Multiplying Decimal Numbers by 10, 100 and 1000

When we multiply by 10, the

number gets 10 times bigger.

Therefore, the number moves one

place to the left on our place

value grid.

When we multiply by 100, the

number gets 100 times bigger.

Therefore, the number moves two

places to the left on our place

value grid.

When we multiply by 1000, the

number gets 1000 times bigger.

Therefore, the number moves

three places to the left on our

place value grid.

Example:

If I multiply 3.24 by 10, all my

counters will move one place to

the left.

My ones will move to the tens,

my tenths will move to the ones,

and my hundredths will move to

the tenths.

3.24 x 10 = 32.4

If I multiply 3.24 by 100, all my counters will move 2 places to

the left. If I multiply 3.24 by 1000, all my

counters will move three places to the

My ones will move to the hundreds, my tenths will move to

left.

the tens and my hundredths will move to the ones.

Can you work out what the answer will

3.24 x 100 = 324

be?

(if you don’t have any decimal values left, you do not have to Do you need to use any place value

include a decimal point in your answer) holders?

2.
Dividing Decimal Numbers by 10, 100 and 1000

When we divide by 10, the

number gets 10 times smaller.

Therefore, the number moves one

place to the right on our place

value grid.

When we divide by 100, the

number gets 100 times smaller.

Therefore, the number moves two

places to the right on our place

value grid.

When we multiply by 1000, the

number gets 1000 times smaller.

Therefore, the number moves

three places to the right on our

place value grid.

If I divide 14.4 by 10, all my counters will

move one place to the right.

My tenths will move to hundredths, my

ones will move to tenths and my tens will

move to the ones.

14.4 ÷ 10 = 1.44

If I divide 14.4 by 100, all my counters will move two

If I divide 14.4 by 1000, all my counters

places to the right.

will move three places to the right.

My tenths will become thousandths, my ones will become

Can you work out what the answer will

hundredths and my tens will become tenths.

be?

14.4 ÷ 100 + 0.144

Where will your place holders need to

Now I no longer have any ones I use 0 as a place holder. go?

Useful videos

This video focuses on whole numbers, rather than decimals. However, it does remind you the rules we use when

we multiply or divide a number by 10 and 100. If you are not confident, I would suggest watching this before

moving onto decimals: https://www.bbc.co.uk/bitesize/topics/z36tyrd/articles/z2fkwxs

In this video, they talk you through multiplying and dividing decimals by 10, 100 and 1000. It might be helpful to

have a pencil and paper or place value grid to hand when you watch it: https://www.youtube.com/watch?v=6fLNcGSa_L4

This video demonstrates how you can use a place value grid to help you:

When we divide by 10, the

number gets 10 times smaller.

Therefore, the number moves one

place to the right on our place

value grid.

When we divide by 100, the

number gets 100 times smaller.

Therefore, the number moves two

places to the right on our place

value grid.

When we multiply by 1000, the

number gets 1000 times smaller.

Therefore, the number moves

three places to the right on our

place value grid.

If I divide 14.4 by 10, all my counters will

move one place to the right.

My tenths will move to hundredths, my

ones will move to tenths and my tens will

move to the ones.

14.4 ÷ 10 = 1.44

If I divide 14.4 by 100, all my counters will move two

If I divide 14.4 by 1000, all my counters

places to the right.

will move three places to the right.

My tenths will become thousandths, my ones will become

Can you work out what the answer will

hundredths and my tens will become tenths.

be?

14.4 ÷ 100 + 0.144

Where will your place holders need to

Now I no longer have any ones I use 0 as a place holder. go?

Useful videos

This video focuses on whole numbers, rather than decimals. However, it does remind you the rules we use when

we multiply or divide a number by 10 and 100. If you are not confident, I would suggest watching this before

moving onto decimals: https://www.bbc.co.uk/bitesize/topics/z36tyrd/articles/z2fkwxs

In this video, they talk you through multiplying and dividing decimals by 10, 100 and 1000. It might be helpful to

have a pencil and paper or place value grid to hand when you watch it: https://www.youtube.com/watch?v=6fLNcGSa_L4

This video demonstrates how you can use a place value grid to help you:

3.
Multiplying and Dividing Decimals - Challenges

We know that lots of you like to take on a challenge during our maths lessons. These challenges are not

compulsory, but are there for anyone who wishes to give them a go. Good luck!

All of these challenges were taken from the

White Rose Maths Hub. They have also

produced a ‘Home Learning’ section to their

website. On here are videos which may help you

with your learning.

https://whiterosemaths.com/homelearning/year-5/

We know that lots of you like to take on a challenge during our maths lessons. These challenges are not

compulsory, but are there for anyone who wishes to give them a go. Good luck!

All of these challenges were taken from the

White Rose Maths Hub. They have also

produced a ‘Home Learning’ section to their

website. On here are videos which may help you

with your learning.

https://whiterosemaths.com/homelearning/year-5/

4.
Place Value Grid

Below is an example of a place value grid taken from Twinkl. You can easily draw your own at home to use or

print off an example from the internet, just make sure it has decimal places on it.

Below is an example of a place value grid taken from Twinkl. You can easily draw your own at home to use or

print off an example from the internet, just make sure it has decimal places on it.