How to find the fractional equivalent of a decimal

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PSAT Math › How to find the fractional equivalent of a decimal

Questions 1 - 2

1

Express as a fraction: $0.3\overline{4}$

$\frac{31}{90}$

$\frac{34}{99}$

$\frac{31}{99}$

$\frac{34}{90}$

$\frac{34}{101}$

Explanation

Let $x = 0.3\overline{4} = 0.3444...$

Then

$10 x = 10 \times 0.3444... = 3.444...$

and

$100 x = 100 \times 0.3444... = 34.44...$

Subtract:

$\underline{10 x = ; ; 3.444...}$

$x = \frac{31}{90}$

2

Write 0.45 as a fraction.

$\frac{9}{20}$

$\frac{3}{4}$

$\frac{2}{5}$

$\frac{11}{20}$

$\frac{5}{9}$

Explanation

.45 is equivalent to 45 out of 100, or $\frac{45}{100}$ .

Divide both the numerator and denominator by 5 to simplify the fraction:

$\frac{9}{20}$

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