 What you need to know

Things to remember:

• The number on top of the 10ths and 100ths go to the right of the decimal after converting.
• If there is a number smaller than 10 on top of the hundredths, there will be an extra zero on the right of the decimal.
• Reading the fraction tells us where the numbers on top go.

This topic is all about turning 10ths and 100ths (fractions) into decimal numbers.

So, how do we turn a fraction into a decimal? Well, we just need to remember that a fraction is another way of writing a division, $\dfrac{6}{10}=6\div10$. But, how do we do divisions? Bus stop method! So, how many 10s can fit into 6? Well, none. 10 is too big. Usually here we’d “carry” how much we had left, but where can we move the 6 to, there’s nowhere to go? Well, we need to put a decimal point and a zero in. Now that we have somewhere to move our 6 to, let’s move it over the decimal! Now that we have moved the 6 to the 0, we have turned it into 60. How many 10s go into 60? 6! So, the answer is 6! Wait, no, there are six 10s in 60, not in 6. We need to put a decimal on top. So, $6\div10=0.6$, or $\dfrac{6}{10}=0.6$.

What is helpful to know, is that the value of the 6 is called “tenths”. So, if we read a fraction like $\dfrac{8}{10}$ as “eight tenths”, we know that the 8 will go after the decimal.

$$\frac{8}{10} = 0.8$$

$$\frac{5}{10} = 0.5$$

$$\frac{4}{10} = 0.4$$

So, if we call the first decimal place tenths, what do you think we call the second one? Well, our normal place values go units, tens, hundred, thousands, etc, and decimal do something similar. Decimals go tenths, hundredths, thousandths, etc.

What is $\dfrac{6}{100}$ as a decimal?

Well, if we read it out loud as “six hundredths”, the 6 will go in the hundredths place value.

$$\frac{6}{100} = 0.06$$

We do the same with other numbers less than 10.

$$\frac{8}{100} = 0.08$$

$$\frac{5}{100} = 0.05$$

$$\frac{4}{100} = 0.04$$

Things get a little different for numbers bigger than 10.

What is $\dfrac{65}{100}$ as a decimal?

Well, $\dfrac{5}{100} = 0.05$ and we have the extra 6, so where do you think that might go? It goes on the left of the 5!

$$\frac{65}{100} = 0.65$$

When there are two numbers on top of a fraction with 100 on the bottom, both numbers go on the right of the decimal!

$$\frac{13}{100} = 0.13$$

$$\frac{38}{100} = 0.38$$

$$\frac{97}{100} = 0.97$$

Example Questions

$$\frac{1}{10} = 0.1$$

$$\frac{26}{100} = 0.26$$