UnknownPhD wrote:

Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 10/189

B. 15/196

C. 16/225

D. 25/144

E. 39/128

Need to know faster way to find the terminating decimal...thanks!

First, terminating decimals have a fixed number of digits after the decimal point.

For eg. 5/2 = 2.5 (this is a terminating decimal)

1/3 = 1.33333333 ( this is recurring decimal)

For a fraction to have terminating decimals, it can have only 2 and/or 5 as prime factors in the denominator ....

If we see all the denominators, we have prime factors other than 2 and 5. Only choice E has only prime factor as 2

A. 10/189 = 2x5/(3x3x3x7) ..... This has 3 and 7. So this will definitely have recurring decimals.

B. 15/196 = 3x5/(2x2x2x2x3x3) ..... This has 2 but this also has 3 which means this will definitely have recurring decimals.

C. 16/225 = 2x2x2x2/(5x5x7) ..... This has 5 but this also has 7 which means this will definitely have recurring decimals.

D. 25/144 = 5x5/(2x2x2x2x3x3) ..... This has 2 but this also has 3 which means this will definitely have recurring decimals.

E. 39/128 = 3x13/(2x2x2x2x2x2x2) -----2. This has ONLY 2. So this HAS to be a terminating decimal

Choice E has to be the right answer.

Hope this helped. If not, let me know.

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