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

# Terminating or Not

##### Age 11 to 14 Challenge 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?

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.