What you need to know

Things to remember:

  • We can think of the fractions as their place values.
  • If there are 0s on the ends of the numbers in the fraction, we can divide by 10.

What is \dfrac{30}{100} as an equivalent fraction in tenths?

Well, let’s think about it. We are told that there are “30 hundredths”, but we know that 10 hundredths make 1 tenth, so how many tenths do we have here?

30\div10=3

30\text{ Hundredths }= 3\text{ Tenths }

Or, if we were to write these both as fractions:

\frac{30}{100}=\frac{3}{10}

Notice how this is the same as just taking a 0 off the top and bottom, which is just dividing both by 10.

\frac{30}{100}=\frac{30\div10}{100\div10}=\frac{3}{10}

And whenever we have 0s on the top and bottom we can do this.

\frac{50}{100}=\frac{50\div10}{100\div10}=\frac{5}{10}

\frac{80}{100}=\frac{80\div10}{100\div10}=\frac{8}{10}

\frac{140}{100}=\frac{140\div10}{100\div10}=\frac{14}{10}

We don’t just have to do this with tenths and hundredths, we can do this for bigger numbers like thousandths too!

\frac{250}{1000}=\frac{250\div10}{1000\div10}=\frac{25}{100}

\frac{600}{1000}=\frac{600\div10}{1000\div10}=\frac{60}{100}

But did we have to stop there? We can divide by 10 again for \frac{60}{100}

\frac{60}{100}=\frac{60\div10}{100\div10}=\frac{6}{10}

\frac{600}{100}=\frac{6}{10}

So, as long as we have 0s at the ends of the numbers in the fraction, we can divide by 10!

Example Questions

Question 1: What is \dfrac{90}{100} in tenths?

Answer

\frac{90}{100}=\frac{90\div10}{100\div10}=\frac{9}{10}

Question 2: What is \dfrac{600}{1000} in tenths?

Answer

\frac{600}{1000}=\frac{600\div10}{1000\div10}=\frac{60}{100}

 

\frac{60}{100}=\frac{60\div10}{100\div10}=\frac{6}{10}

 

\frac{600}{1000}=\frac{6}{10}