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ACT Math : How to find the decimal equivalent of a fraction

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Example Questions

Example Question #251 : Arithmetic

When 5/11 is written as a decimal, what is the 100th digit to the right of the decimal point?

Possible Answers:

Correct answer:

Explanation:

When 5 is divided by 11, the decimal is 0.45 repeating, with a 5 in the hundreths place. The key here is to recognize that 100 is an even number, and the 5 in 0.45 is two places to the right of the decimal point (2 also being an even number).

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Example Question #1 : Decimals

Find the sum of the following:

$5\frac{1}{8}+6\frac{3}{16}?$ $\displaystyle 5\frac{1}{8}+6\frac{3}{16}?$

Possible Answers:

11.1875 $\displaystyle 11.1875$

11.3125 $\displaystyle 11.3125$

11.25 $\displaystyle 11.25$

11.125 $\displaystyle 11.125$

11.625 $\displaystyle 11.625$

Correct answer:

11.3125 $\displaystyle 11.3125$

Explanation:

To get the decimal from a fraction, divide the numerator by the denominator

$\frac{1}{8}=0.125$ $\displaystyle \frac{1}{8}=0.125$

$5\frac{1}{8}=5.125$ $\displaystyle 5\frac{1}{8}=5.125$

$\frac{3}{16}=0.1875$ $\displaystyle \frac{3}{16}=0.1875$

$6\frac{3}{16}=6.1875$ $\displaystyle 6\frac{3}{16}=6.1875$

$\displaystyle 5.125+6.1875=11.3125$

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Example Question #251 : Arithmetic

Find the sum to the nearest hundredth:

$13\frac{3}{8} + 12\frac{17}{40} ?$ $\displaystyle 13\frac{3}{8} + 12\frac{17}{40} ?$

Possible Answers:

26.3 $\displaystyle 26.3$

27.4 $\displaystyle 27.4$

28.9 $\displaystyle 28.9$

25.8 $\displaystyle 25.8$

24.3 $\displaystyle 24.3$

Correct answer:

25.8 $\displaystyle 25.8$

Explanation:

1. Convert the fractions to decimals by division:

$\frac{3}{8}=0.375$ $\displaystyle \frac{3}{8}=0.375$

$\frac{17}{40}=0.425$ $\displaystyle \frac{17}{40}=0.425$

2. Add the corresponding whole numbers to the decimals:

$\displaystyle 13+0.375=13.375$

$\displaystyle 12+0.425=12.425$

3. Add the two decimals:

$\displaystyle 13.375 + 12.425 = 25.8$

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Example Question #1 : Decimals

If $\frac{1}{3} < x < 0.76$ $\displaystyle \frac{1}{3} < x < 0.76$, $\displaystyle x$ can equal which of the following?

Possible Answers:

$\frac{5}{16}$ $\displaystyle \frac{5}{16}$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

None of the other answer choices are correct

$\frac{4}{12}$ $\displaystyle \frac{4}{12}$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

Correct answer:

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

Explanation:

Convert all of the fractions to decimals. Thus, x is contained within the range of 0.33 < x < 0.76. The answers choices become 1/4 = 0.25, 4/12 = 0.33, 2/5 = 0.4, and 5/16 = 0.3125, respectively. Therefore, the only answer which is within the desired range is 2/5.

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ACT Math : How to find the decimal equivalent of a fraction

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #251 : Arithmetic

Example Question #1 : Decimals

Example Question #251 : Arithmetic

Example Question #1 : Decimals

All ACT Math Resources

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