How to find the decimal equivalent of a fraction - SSAT Middle Level Math

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Question

Which of the following is NOT equal to $0.5 \bullet 20$ ?

Answer

All of the answer choices multiply to give you 10 except

$\frac{3}{4} \bullet 16$

so that is the correct answer.

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Question

What fractions equals ?

Answer

is equal to $\frac{1}{2}$ .

Thus we are looking for a fraction that reduces to $\frac{1}{2}$ .

$\frac{8}{12}$ reduces to $\frac{2}{3}$ (divide numerator and denominator by 4).

$\frac{8}{4}$ reduces to 2 (divide numerator and denominator by 4).

$\frac{8}{2}$ reduces to 4 (divide numerator and denominator by 2).

$\frac{8}{32}$ reduces $\frac{1}{4}$ (divide numerator and denominator by 4).

$\frac{8}{16}$ is the only one that reduces to $\frac{1}{2}$ (divide numerator and denominator by 8).

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Question

Write 0.74 as a fraction in lowest terms.

Answer

This decimal has its last nonzero digit in the hundredths place; this number is equal to "seventy-four one-hundredths". As a fraction, this is

$\frac{74}{100}$

This is not in lowest terms, since .

Reduce:

$\frac{74}{100} = \frac{74\div 2}{100\div 2} = \frac{37}{50}$

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Question

Write the decimal equivalent of $\frac{3}{400}$ .

Answer

$\frac{3}{400} = 3 \div 400 = 0.0075$

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Question

Express 0.014 as a fraction in lowest terms.

Answer

The fraction has its last nonzero digit in the thousandths place, so write the number, without the decimal point, over 1,000. Then reduce.

$\frac{14}{1,000} =\frac{14\div 2}{1,000\div 2} = \frac{7}{500}$

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Question

Express $\frac{3}{400}$ as a decimal.

Answer

$\frac{3}{400} = 3 \div 400 = 0.0075$

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Question

Write as a decimal:

$\frac{5}{9}$

Answer

$5 \div 9 = 0.5555...$

That is, the digit 5 will repeat infinitely. This can be written as $0.\overline{5}$ .

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Question

Write as a decimal:

$\frac{9}{11}$

Answer

$9 \div 11 = 0.81818181...$

That is, the group "81" will repeat infinitely. This quotient can be written as $0.\overline{81}$ .

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Question

Rewrite as a decimal:

$\frac{7}{12}$

Answer

$7 \div 12 = 0.583333...$

That is, after 5 and 8, the digit 3 will repeat infinitely. This can be rewritten as $0.58\overline{3}$ .

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Question

Write as a decimal:

$\frac{5}{18}$

Answer

$5 \div 18 = 0.27777...$

That is, after the 2, the digit 7 repeats infinitely. This can be rewritten as $0.2\overline{7}$ .

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Question

Express $\frac{9}{20}$ as a decimal.

Answer

Divide the numerator by the denominator:

$9 \div 20 = 0.45$

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Question

Express as a fraction in simplest form.

Answer

is forty-four one-hundredths, so write this as a fraction and reduce:

$\frac{44}{100} = \frac{44\div 4}{100\div 4} = \frac{11}{25}$

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Question

$10 +\tfrac{3}{20}$

Answer

The question is asking you to add the two numbers and find its equivalent in decimal form. Naturally,

$10 + \tfrac{3}{20} = 10 \tfrac{3}{20}$

We must find out how to represent $\tfrac{3}{20}$ as a decimal in order to solve the problem. To find the decimal form, divide 1.00 by 20.

$1.00 \div 20 = 0.05$

You divide by 1.00 because decimals are based off of this number (fractions are based on 1 and percents on 100%). The answer is exactly $\tfrac{1}{20}$ . In order to figure out what the equivalent of $\tfrac{3}{20}$ is, simply multiply your answer by the numerator, 3.

$3 \times 0.05 = 0.15$

Your answer is

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Question

Write as a fraction in lowest terms: $0.2\overline{6}$

Answer

We can use algebra to find the fraction by setting $N = 0.2\overline{6}$ . Then:

$100 \cdot N = 100 \cdot 0.2666...$

and

$10 \cdot N = 10 \cdot 0.2666...$

Subtract as follows:

$\underline{-10N = 2.666}$

$90N \div 90 = 24\div 90$

$N = \frac {24}{90} = \frac {24 \div 6}{90\div 6} = \frac {4}{15}$

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Question

Write as a decimal: $\frac{23}{30}$

Answer

Divide by :

$23 \div 30 = 0.7666...$

The 6 repeats infinitely, so this can be written as $0.7\overline{6}$

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Question

What is the decimal equivalent of $\frac{2}{5}$ ?

Answer

To find the decimal equivalent of a fraction, convert the fraction's denominator to a factor of . In this problem, we can convert the denominator to by multiplying both the top and bottom of the fraction by :

$\frac{2}{5}\cdot\frac{2}{2}=\frac{4}{10}$ , which is equivalent to

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Question

What is the decimal equivalent of $\frac{3}{5}$ ?

Answer

To find the decimal equivalent of a fraction, convert the denominator of the fraction to a factor of .

$\frac{3}{5}=\frac{6}{10}$ , which is equal to .

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Question

Arrange these numbers from least to greatest:

$\left { \frac{6}{7}, \frac{17}{20}, \frac{9}{11} \right }$

Answer

Rewrite all three numbers as their decimal equivalents by dividing numerator by denominator.

$\frac{6}{7} = 6 \div 7 = 0.857142...$

$\frac{17}{20} = 17 \div 20 = 0.85$

$\frac{9}{11} = 9 \div 11 = 0.8181...$

From the decimal equivalents, the fractions can be arranged as follows:

$\left {\frac{9}{11}, \frac{17}{20}, \frac{6}{7}\right }$

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Question

Arrange these numbers from least to greatest:

$\left { -\frac{3}{5}, -\frac{13}{20}, -\frac{16}{25} \right }$

Answer

Rewrite all three numbers as their decimal equivalents by dividing numerator by denominator.

$-\frac{3}{5} = -3 \div 5 = -0.6$

$-\frac{13}{20} = -13 \div 20 = - 0.65$

$-\frac{16}{25} = -16 \div 25 = -0.64$

To arrange negative numbers from least to greatest, we must arrange them so that their absolute values (values without the negative symbol) go from greatest to least. In descending order, the absolute values are

$\left { 0.65, 0.64, 0.6\right }$

so, in ascending order, the numbers themselves are

$\left { -0.65,- 0.64,- 0.6\right }$ ,

or, as fractions,

$\left { -\frac{13}{20}, -\frac{16}{25}, -\frac{3}{5} \right }$ .

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Question

Write $\frac{11}{12}$ as a decimal.

Answer

Divide 11 by 12.

$11 \div 12 = 0.91666...$

Note that the "6" repeats forever. This can be written as $0.91\overline{6}$ .

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