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Weekly Problem 24 - 2012
Can you put these very close fractions into order?

# Terminating or Not

##### Age 11 to 14Challenge Level

A terminating decimal is a decimal which has a finite number of decimal places, such as 0.25, 0.047, or 0.7734

Take a look at the fractions below.

$$\frac23 \qquad \frac45 \qquad \frac{17}{50} \qquad \frac3{16}$$ $$\frac7{12} \qquad \frac58 \qquad \frac{11}{14} \qquad \frac8{15}$$

Which ones do you think can be written as a terminating decimal?

Click below to check which ones terminate.

Four of the fractions can be written as terminating decimals: $$\frac45=\frac8{10}=0.8$$ $$\frac{17}{50}=\frac{34}{100}=0.34$$ $$\frac{3}{16}=\frac{1875}{10000}=0.1875$$ $$\frac58=\frac{625}{1000}=0.625$$ The remaining four fractions can be written as recurring decimals, with a repeating pattern that goes on forever.

I wonder whether there is a quick way to decide whether a fraction can be written as a terminating decimal...

Choose some fractions, convert them to decimals, and write down the fractions whose decimals terminate.
What do they have in common?

Can you explain a method you could use to identify fractions which can be written as terminating decimals?

Next you might like to explore recurring decimals in the problem Repetitiously.

You may also be interested in the other problems in our Comparing and Matching Feature.