Which of these fractions have a decimal that ends: 13/32, 7/15, 35/56, 17/125?
Contributed by StemPy LabTry 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: , , , ? Do not divide. Look at the bottoms, after putting each fraction in lowest terms. Then give the decimal of .
Need a reminder? The key ideaShow
A rational number is , with integers and and . Its decimal ends or repeats. In lowest terms, it ends exactly when the bottom has no prime factor other than and .
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.
Step 1. . . It ends.
Step 2. . . The makes it repeat.
Step 3. . It reduces to , and . It ends: .
Step 4. . . It ends.
Answer: three of them end; only repeats. .
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