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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Question

Rewrite $\frac{5}{8}$ as a decimal.

Answer

Divide by ; the result is .

You may also recognize that $\frac{1}{8}$ is equal to , and $\frac{5}{8}$ will be equal to times this value.

$\frac{5}{8}=5\frac{1}{8}=5(0.125)=0.625$

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Question

How do you write 0.125 as a fraction?

Answer

$0.125=\frac{125}{1000}=\frac{1}{8}$

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Question

Write the decimal equivalent of $\frac{3}{500}$ .

Answer

$\frac{3}{500} = 3 \div 500 = 0.006$

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Question

Express $\frac{9}{25}$ as a decimal.

Answer

Divide the numerator by the denominator:

$9 \div 25 = 0.36$

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Question

Express 0.36 as a fraction in simplest form.

Answer

Write the expression, without the decimal point (36), over the apporpriate power of 10 (100, since the last digit falls in the hundredths place). Then reduce:

$\frac{36}{100} = \frac{36\div 4}{100\div 4} = \frac{9}{25}$

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Question

Express as a simplified fraction.

Answer

In order to express as a fraction, we first put $\small 634$ in as the numerator for our fraction. For the denominator we use because the last digit of is in the thousandths place.

$\small \frac{634}{1000}$

Since both numbers are even, we can reduce both the numerator and the denomintor by dividing by $\small 2$ .

$\small \small 634/2=317$

$\small 1000/2=500$

Now our answer becomes $\small \frac{317}{500}$ .

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