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

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Example Question #1312 : Numbers And Operations

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

Possible Answers:

$\frac {5}{33}$

$\frac {4}{15}$

$\frac {29}{99}$

$\frac {2}{15}$

$\frac {13}{50}$

Correct answer:

$\frac {4}{15}$

Explanation:

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

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

100N = 26.666...

and

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

10N = 2.666...

Subtract as follows:

100N = 26.666...

$\underline{-10N = 2.666}$

90N = 24

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

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

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Example Question #12 : How To Find The Decimal Equivalent Of A Fraction

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

Possible Answers:

10.15

10.30

10.20

10.05

Correct answer:

10.15

Explanation:

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 0.05 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 10.15

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Example Question #1311 : Numbers And Operations

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

Possible Answers:

0.2

0.4

4.4

0.5

0.52

Correct answer:

0.4

Explanation:

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 0.4

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Example Question #14 : How To Find The Decimal Equivalent Of A Fraction

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

Possible Answers:

0.6

0.5

1.6

1.3

0.4

Correct answer:

0.6

Explanation:

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 0.6 .

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Example Question #831 : Fractions

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

Possible Answers:

0.916

$0.9\overline{1}$

0.9167

$0.91\overline{67}$

$0.91\overline{6}$

Correct answer:

$0.91\overline{6}$

Explanation:

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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Example Question #16 : How To Find The Decimal Equivalent Of A Fraction

Arrange these numbers from least to greatest:

$\left \{ -0.44404, -0.44044, -0.40444, \right \}$

Possible Answers:

$\left \{ -0.44404, -0.44044, -0.40444 \right \}$

$\left \{ -0.40444,-0.44404, -0.44044 \right \}$

$\left \{ -0.40444 , -0.44404, -0.44044\right \}$

$\left \{ -0.44404,-0.40444, -0.44044 \right \}$

$\left \{ -0.40444,-0.44044, -0.44404 \right \}$

Correct answer:

$\left \{ -0.44404, -0.44044, -0.40444 \right \}$

Explanation:

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.

$\left \{ 0.44404, 0.44044, 0.40444 \right \}$

This can be done by going from right to left starting with the units digit. The units and tenths digits are the same, but the hundredths digit of 0.40444 is the least, so this number is less than the other two. The thousandths digit of 0.44044 is less than that of 0.44404, so it is the lesser of the two that remain. Therefore, in descending order, the absolute values are

$\left \{ 0.44404, 0.44044, 0.40444 \right \}$ ,

and in ascending order, the numbers are

$\left \{ -0.44404, -0.44044, -0.40444 \right \}$ .

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Example Question #832 : Fractions

How many of the following four numbers are elements of the set $B = \left \{ x \; | \; \frac{2}{5}< x < \frac{3}{5}\right \} ?$ ?

(A) 0.44

(B) 0.55

(D) 0.77

Possible Answers:

Two

None

Four

Three

One

Correct answer:

Two

Explanation:

$\frac{2}{5} = 2 \div 5 = 0.4$ and $\frac{3}{5} = 3 \div 5 = 0.6$ , so we are looking for numbers that fall between 0.4 and 0.6 exclusive. Of the four choices, 0.44 and 0.55 fall between these numbers. The correct response is two.

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Example Question #18 : How To Find The Decimal Equivalent Of A Fraction

Arrange these numbers from least to greatest:

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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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Example Question #11 : How To Find The Decimal Equivalent Of A Fraction

Arrange these numbers from least to greatest:

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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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Example Question #12 : How To Find The Decimal Equivalent Of A Fraction

Express 0.44 as a fraction in simplest form.

Possible Answers:

$\frac{11}{20}$

$\frac{22}{45}$

$\frac{11}{24}$

$\frac{11}{25}$

$\frac{22}{50}$

Correct answer:

$\frac{11}{25}$

Explanation:

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

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #1312 : Numbers And Operations

Example Question #12 : How To Find The Decimal Equivalent Of A Fraction

Example Question #1311 : Numbers And Operations

Example Question #14 : How To Find The Decimal Equivalent Of A Fraction

Example Question #831 : Fractions

Example Question #16 : How To Find The Decimal Equivalent Of A Fraction

Example Question #832 : Fractions

Example Question #18 : How To Find The Decimal Equivalent Of A Fraction

Example Question #11 : How To Find The Decimal Equivalent Of A Fraction

Example Question #12 : How To Find The Decimal Equivalent Of A Fraction

All SSAT Middle Level Math Resources

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