How to find the decimal equivalent of a fraction - ISEE Middle Level Quantitative Reasoning

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Question

Express as a fraction.

Answer

The last nonzero digit is in the ten-thousandths place, so write the number, without decimal point or leading zeroes, over 10,000. Then reduce.

$\frac{25}{10,000} = \frac{25 \div 25}{10,000\div 25} = \frac{1}{400}$

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Question

Which is the greater quantity?

(a) $\frac{1}{7}$

(b)

Answer

Divide 1 by 7:

$\frac{1}{7} = 1 \div 7 = 0.142857... < 0.143$

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Question

Which is the greater quantity?

(a) $\frac{7}{11}$

(b)

Answer

Divide 7 by 11:

$\frac{7}{11} = 7 \div 11 = 0.636363... > 0.63$

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Question

Which is the greater quantity?

(a) $- \frac{3}{13}$

(b)

Answer

Divide 3 by 13:

$\frac{3}{13} = 3 \div 13 = 0.230769... > 0.23$

$\frac{3}{13} > 0.23 \Rightarrow -\frac{3}{13} < - 0.23$

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Question

Which is the greater quantity?

(a) $- \frac{7}{12}$

(b)

Answer

Divide 7 by 12:

$7 \div 12 = 0.58333... > 0.58$

$\frac{7 }{12} > 0.58$ , so $- \frac{7 }{12} < - 0.58$

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Question

Column A Column B

$\frac{9}{25}$

Answer

There are two ways to solve this problem. You can convert both to either fractions or decimals so that you can properly compare them. If you want to compare them as decimals, convert Column B to a decimal by dividing 9 by 25, which gives you 0.36. Then, you can see that Column A is greater. If you want to look at both as fractions, put 68 over 100 to get $\frac{68}{100}.$ This can be further simplifies to $\frac{17}{25}.$ Therefore, you can see that Column A is greater.

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Question

Give the answer as a decimal:

$\frac{1}{5} + \frac{1}{4} - \frac{1}{10}$

Answer

$\frac{1}{5} = 1 \div 5 = 0.2$

$\frac{1}{4} = 1 \div 4 = 0.25$

$\frac{1}{10} = 1 \div 10 = 0.1$

$\frac{1}{5} + \frac{1}{4} - \frac{1}{10} = 0.2 + 0.25 - 0.1 = 0.45 - 0.1 = 0.35$

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Question

Give the result as a decimal:

$\frac{4}{5} + \frac{3}{4} \cdot \frac{1}{2}$

Answer

$\frac{4}{5} + \frac{3}{4} \cdot \frac{1}{2}$

$= \frac{4}{5} + \frac{3\cdot 1}{4\cdot 2}$

$= \frac{4}{5} + \frac{3 }{8}$

$= \frac{4\cdot 8}{5 \cdot 8} + \frac{5 \cdot 3 }{5 \cdot8}$

$= \frac{32}{40} + \frac{15}{40} = \frac{32+ 15 }{40} = \frac{47 }{40}$

$\frac{47 }{40} = 47 \div 40 = 1.175$

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Question

Give the answer as a decimal:

$\left (\frac{3}{4} \right )^{2}$

Answer

$\left (\frac{3}{4} \right )^{2} = \frac{3^{2}}{4^{2}} = \frac{9}{16} = 9 \div 16 = 0.5625$

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Question

Give the result as a decimal:

$2-\left ( \frac{3}{2} \right )^{2}$

Answer

$2-\left ( \frac{3}{2} \right )^{2}$

Square the fraction by squaring both the numerator and the denominator.

$2-\left ( \frac{3^{2}}{2^{2}} \right )$

$2- \frac{9}{4}$

To subtract, convert so that each term shares a common denominator.

$\frac{8}{4}- \frac{9}{4}$

$\frac{8-9}{4}$

$\frac{-1}{4}$

$-\frac{1}{4}$

Finally, convert to a decimal.

$- \frac{1}{4} = -1 \div 4 = -0.25$

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Question

Write the result as a decimal:

$10 - \left ( 2 \frac{1}{2}\right )^{2}$

Answer

$10 - \left ( 2 \frac{1}{2}\right )^{2}$

First, evaluate the term in parenthesis:

$10 - \left ( \frac{2 \times 2 + 1}{2}\right )^{2}$

$10 - \left ( \frac{5}{2}\right )^{2}$

Apply the exponent by sparing the numerator and the denominator.

$10 - \left ( \frac{5^{2}}{2^{2}}\right )$

$10 - \frac{25}{4}$

To subtract, convert the terms to a common denominator.

$\frac{40}{4} - \frac{25}{4}$

$\frac{40-25}{4}$

$\frac{15}{4}$

Divide to convert the fraction to a decimal.

$15 \div 4 = 3.75$

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Question

and are positive.

$0.66 x = \frac{2}{3} y$

Which is the greater quantity?

(a)

(b)

Answer

This can be solved by noting that, converting the decimal to a fraction, $0.66 = \frac{66}{100}$ .

The equation can be rewritten as

$\frac{66}{100}x = \frac{2}{3} y$

Multiply both sides by $\frac{100}{66 }$ :

$\frac{100}{66 } \cdot \frac{66}{100}x =\frac{100}{66 } \cdot \frac{2}{3} y$

$x =\frac{200}{198} y$

$\frac{200}{198} > 1$ , so

$\frac{200}{198} y > 1y$ , and

.

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Question

and are positive.

$\frac{1}{8} x = 0 .125 y$

Which is the greater quantity?

(a)

(b)

Answer

Multiply both sides by 8, and the following is revealed:

$\frac{1}{8} x = 0 .125 y$

$\frac{x }{8} = 0 .125 y$

$\frac{x }{8} \cdot 8 = 0 .125 y \cdot 8$

On the left side, the division is cancelled by the multiplication. On the right, $0.125 \cdot 8 = 1$ , so

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Question

Express as a fraction.

Answer

The last nonzero digit is in the ten-thousandths place, so write the number, without decimal point or leading zeroes, over 10,000. Then reduce.

$\frac{25}{10,000} = \frac{25 \div 25}{10,000\div 25} = \frac{1}{400}$

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