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GED Math : Decimal and Fraction Conversions

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Example Questions

Example Question #1 : Decimal And Fraction Conversions

Express as a fraction: $0.\overline{42}$

Possible Answers:

$\frac{42}{101}$

$\frac{21}{50}$

$\frac{14}{33}$

$\frac{7}{15}$

Correct answer:

$\frac{14}{33}$

Explanation:

Let $x = 0.\overline{42} = 0.424242...$

Then $100x = 100 \times 0.424242... = 42.424242...$

Subtract:

100x = 42.424242...

$\underline{x = 0.424242...}$

99x = 42

$x = \frac{42}{99} = \frac{42 \div 3}{99 \div 3} = \frac{14}{33}$

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Example Question #1 : Decimal And Fraction Conversions

Express as a decimal: $\frac{15}{16}$

Possible Answers:

$0.9\overline{3}$

$1.0\overline{7}$

$1.0\overline{6}$

0.9375

Correct answer:

0.9375

Explanation:

Divide 15 by 16:

Division

$\frac{15}{16} = 0.975$

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Example Question #2 : Decimal And Fraction Conversions

Express as a fraction:

$0.4\overline{7}$

Possible Answers:

$\frac{47}{99}$

$\frac{7}{15}$

$\frac{43}{90}$

$\frac{47}{101}$

Correct answer:

$\frac{43}{90}$

Explanation:

Let $x=0.4\overline{7} = 0.4777...$

Then

$10x = 10 \times 0.4777... = 4.7777...$

and

$100x = 100 \times 0.4777... = 47.777...$

We can subtract:

100x= 47.777...

$\underline{10x = \; \; 4.777...}$

90x = 43

$x = \frac{43}{90}$

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Example Question #2 : Decimal And Fraction Conversions

Which number has 5.25 as its reciprocal?

Do not use a calculator.

Possible Answers:

-5.25

$1\frac{4}{5}$

$\frac{4}{21}$

$\frac{21}{4}$

Correct answer:

$\frac{4}{21}$

Explanation:

The number that has 5.25 as its reciprocal is, in return, the reciprocal of 5.25.

Convert 5.25 to a fraction:

$5.25 = \frac{525 }{100} = \frac{525 \div 25 }{100\div 25 } = \frac{21}{4}$

Switch the numerator and the denominator to obtain the reciprocal - this number is $\frac{4}{21}$ .

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Example Question #123 : Complex Operations

Which of the following numbers has $\frac{8}{29}$ as its reciprocal?

Do not use a calculator.

Possible Answers:

2.98

3.3

3.625

8.29

Correct answer:

3.625

Explanation:

The number that has $\frac{8}{29}$ as its reciprocal is, in return, the reciprocal of $\frac{8}{29}$ . This number is the result of switching the numerator and denominator - $\frac{29}{8}$ . Since we are looking for the decimal equivalent, we divide 29 by 8:

Division

$29 \div 8 = 3.625$ , the correct choice.

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Example Question #2 : Decimal And Fraction Conversions

Express as a decimal: $\frac{11}{12}$

Possible Answers:

$0.91\overline{6}$

$0.9\overline{2}$

$1.\overline{1}$

$1.\overline{09}$

Correct answer:

$0.91\overline{6}$

Explanation:

Divide 11 by 12:

Division

The "6" repeats forever, so

$\frac{11}{12} = 0.91\overline{6}$ .

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Example Question #4 : Decimal And Fraction Conversions

Express as a decimal: $\frac{16}{15}$

Possible Answers:

$1.0\overline{7}$

0.9375

$0.9\overline{3}$

$1.0\overline{6}$

Correct answer:

$1.0\overline{6}$

Explanation:

Divide 16 by 15:

Division

The "6" repeats forever, so

$\frac{16}{15} = 1.0\overline{6}$ .

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Example Question #5 : Decimal And Fraction Conversions

Express as a decimal: $\frac{12}{11}$

Possible Answers:

$1.\overline{09}$

$0.91\overline{6}$

$1.\overline{1}$

$0.9\overline{2}$

Correct answer:

$1.\overline{09}$

Explanation:

Divide 12 by 11:

Division

The "09" repeasts forever, so

$\frac{12}{11} = 1.\overline{09}$ .

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Example Question #126 : Complex Operations

What is the decimal represented by the fraction $\frac{7}{50}$ ?

Possible Answers:

0.014

0.0014

0.14

1.4

Correct answer:

0.14

Explanation:

Set up a proportion such that this fraction is some number over 100.

$\frac{7}{50} = \frac{x}{100}$

Cross multiply.

700 = 50x

Divide by 50 on both sides.

$\frac{700}{50} = \frac{50x}{50}$

x=14

$\frac{14}{100} = 0.14$

The answer is: 0.14

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Example Question #6 : Decimal And Fraction Conversions

Rewrite 0.24 as a fraction in simplest form.

Possible Answers:

$\frac{5}{18}$

$\frac{6}{25}$

$\frac{3}{10}$

$\frac{7}{24}$

Correct answer:

$\frac{6}{25}$

Explanation:

The last nonzero digit of 0.24 - namely, the "4" - is in the hundredths place, so the fractional representation is

$\frac{24}{100}$

Reduce this to simplest form by dividing both halves by their greatest common factor, which is 4:

$\frac{24}{100} = \frac{24 \div 4}{100\div 4} = \frac{6}{25}$

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All GED Math Resources

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GED Math : Decimal and Fraction Conversions

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1 : Decimal And Fraction Conversions

Example Question #1 : Decimal And Fraction Conversions

Example Question #2 : Decimal And Fraction Conversions

Example Question #2 : Decimal And Fraction Conversions

Example Question #123 : Complex Operations

Example Question #2 : Decimal And Fraction Conversions

Example Question #4 : Decimal And Fraction Conversions

Example Question #5 : Decimal And Fraction Conversions

Example Question #126 : Complex Operations

Example Question #6 : Decimal And Fraction Conversions

All GED Math Resources

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