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How to Solve GMAT Terminating and Repeating Decimals?

Solving decimals can be the trickiest part of the GMAT Math. But to reach the perfect score, one needs to master even the tricky parts. If decimals are bothering you, here are some shortcuts and tricks to solve GMAT Terminating and Repeating Decimals. Before heading to the shortcuts first understand decimals and their types.

GMAT Math Terminating and Repeating Decimals – GT Prep

Rational Numbers: 

A rational number is nothing but the ratio of two integers. Integers are the set of positive and negative whole numbers including zero. It means, {……, -3, -2, -1, 0, 1, 2, 3, 4.....}. So the ratio of two integers gives a rational number. Rational numbers include all fractions along with integers because 4/1=4.

Decimals from rational numbers:

Let us understand the basics of decimals once again. When a decimal is made out of a fraction, it either terminates or repeats. Only these chances are there for decimals. Understand the concept of fractions to score more in the GMAT Math section.

Terminating decimals means,

½ =0.5

1/8 = 0.125

3/20 = 0.15

Repeating decimals means,

1/3 = 0.3333333333333333

1/7 = 0.1428571428571429

1/9 = 0.1111111111111111

How to solve Terminating and Repeating Decimals on GMAT?

A secret of the GMAT exam is there will not be any question like “what is the decimal expression of 7/68?” Mostly the questions will be like “Is the decimal expression for this fraction terminating or repeating?”

Tips to find the terminating and repeating decimals:

1.       Simplify the decimal to the lower fraction and check the denominator. If the denominator has the factors of only 2 and 5, then the decimal is terminating.

Example: 47/1250 – here the denominator has the factor of 2 and 5 which indicates the decimal expression terminating = 0.0376

[Read more: Most Important GMAT Quantitative Reasoning Question Types]

2.       If the denominator has prime factors other than 2 and 5, then it will have decimals repeating.

Examples:

1/32 – Terminates (factor of 2)

1/27 – repeats (has a factor of 3)

1/55 – repeats (has a factor of 11)

1/5 – terminator (has a factor of 5)

3.       There is nothing to do with numerator because; the answer would be the same even the numerator is 1 or 658. No matter how big the numerator is, if the denominator has prime factors as only 2 and 5, then the decimal would be terminating.

4.       Never waste the time on solving the decimals, as it takes so much time to figure out for higher fractions.

5.       Have these shortcuts for fractions handy to get the answer quickly in GMAT.

½ = 0.5

1/3 = 0.3333333333333333

¼= 0.25

1/5= 0.2

1/6= 0.1666666666666667

1/7= 0.1428571428571429

1/8=0.125

1/9= 0.1111111111111111

1/11= 0.0909090909090909

Hard work is needed to succeed. But at the same time, smart work is what can make you stand ahead of anyone and that is what is tested in GMAT. For more tips from the experts, check our GMAT Coaching sessions.

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