Decimals

Lesson

We've already looked at how to divide and, up until now, our answers have always been whole numbers. Now we are going to look at division questions that have decimal answers.

Remember that when we write a decimal, the digits that we write go in certain columns.

This number is $12.9$12.9. It has a $1$1 in the tens column, a $2$2 in the units column, and a $9$9 in the tenths column. The rest of the columns have nothing, or zero, in them (even though we don't normally write all these zeros).

Now, let's say we have $5$5 tens.

What happens if we divide these $5$5 tens by $10$10?

Well, we end up with $5$5 ones!

What about if we have $3$3 hundreds? What happens when we divide this by $10$10?

We end up with $3$3 tens!

Do you see a pattern?

Remember!

Whenever we divide by $10$10, we move down ONE column!

Hundreds become tens, tens become units, units become tenths, and so on.

... |
→ |
Hundreds |
→ |
Tens |
→ |
Units |
→ |
Tenths |
→ |
... |

Let's say we have the number $128$128, and we want to divide it by $10$10.

$128$128 has:

- $1$1 hundred, which will become $1$1 ten.
- $2$2 tens, which will become $2$2 ones.
- $8$8 units, which will become $8$8 tenths.

So, we just move the digits like so.

We just shifted all the digits down a column to the right! This gives us our answer $128\div10=12.8$128÷10=12.8.

Now, what happens when we have $3$3 hundreds and we want to divide this by $100$100?

Well, end up with $3$3 ones!

What's the pattern now?

Remember!

Whenever we divide by $100$100, we move down TWO columns!

Hundreds become units, tens become tenths, units become hundredths, and so on.

... |
→ |
Hundreds |
→ |
Units | → |
Hundredths |
→ |
Ten-Thousandths |
→ |
... |

What's $79\div100$79÷100?.

$79$79 has:

- $7$7 tens, which will become $7$7 tenths.
- $9$9 units, which will become $9$9 thousandths.

So, we just move the digits two columns down to the right!

There is a simple rule we can use for dividing any decimal by $10$10, $100$100, $1000$1000, $10000$10000, etc.

Remember!

Whenever we divide a decimal by $10$10, $100$100, $1000$1000, $10000$10000, etc, we just shift the digits to the right through the decimal point.

The amount of columns the digits move will be the same as the amount of zeros in the divisor!

Try using the GeoGebra Applet below to see this for yourself!

Whenever you're dividing a decimal by any whole number, you can just perform long division as usual, as if the decimal point isn't there! Let's try an example.

We want to find $6\div4$6÷4.

Choose the most reasonable estimate for $6\div4$6÷4.

Between $5$5 and $10$10

ABetween $1$1 and $5$5

BBetween $0$0 and $1$1

CBetween $5$5 and $10$10

ABetween $1$1 and $5$5

BBetween $0$0 and $1$1

CComplete the long division to find $6\div4$6÷4.

$\editable{}$ $.$. $\editable{}$ $4$4 $6$6 $.$. $0$0 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$

What is $13\div10^3$13÷103? Write your answer in decimal form.

What is $0.68\div10^2$0.68÷102? Write your answer in decimal form.

Understand operations on fractions, decimals, percentages, and integers