MediumMathematicsHigh School (9–10)GeneralNumber Systems › Rational and Irrational NumbersNumericalBoard Exam

Which of these fractions have a decimal that ends: 13/32, 7/15, 35/56, 17/125? …

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Which of these fractions have a decimal that ends: $\dfrac{13}{32}$ , $\dfrac{7}{15}$ , $\dfrac{35}{56}$ , $\dfrac{17}{125}$ ? Do not divide. Look at the bottoms, after putting each fraction in lowest terms. Then give the decimal of $\dfrac{35}{56}$ .

Need a reminder? The key ideaShow

A rational number is $\dfrac{p}{q}$ , with integers $p$ and $q$ and $q \neq 0$ . Its decimal ends or repeats. In lowest terms, it ends exactly when the bottom has no prime factor other than $2$ and $5$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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