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Matching Fractions, Decimals and Percentages

Can you match pairs of fractions, decimals and percentages, and beat your previous scores?

Sept 03

What is the last digit of the number 1 / 5^903 ?

Too Close to Call

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? 

Once you've made your predictions, convert the fractions to decimals.

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.