ACT Math - Decimals with Fractions

Find the sum of the following:

$5\frac{1}{8}+6\frac{3}{16}?$

Explanation

To get the decimal from a fraction, divide the numerator by the denominator

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

$5\frac{1}{8}=5.125$

$\frac{3}{16}=0.1875$

$6\frac{3}{16}=6.1875$

When 5/11 is written as a decimal, what is the 100th digit to the right of the decimal point?

Explanation

When 5 is divided by 11, the decimal is 0.45 repeating, with a 5 in the hundreths place. The key here is to recognize that 100 is an even number, and the 5 in 0.45 is two places to the right of the decimal point (2 also being an even number).

What is the fractional equivalent of the sum ?

$\frac{11}{40}$

$\frac{9}{40}$

$\frac{275}{999}$

$\frac{225}{999}$

$\frac{21}{80}$

Explanation

First simplify .

Since has a decimal 3 places from the right, divide this number by , and move the numerator decimal 3 places to the right. As a result:

$0.275=\frac{275}{1000}$

This fraction can be reduced fully by using common factors. Simplify.

$\frac{275}{1000} = \frac{25 \cdot 11}{25 \cdot 40} = \frac{11}{40}$

Convert to a fraction.

$\frac{11}{100}$

$\frac{11}{10}$

$\frac{1}{9}$

$\frac{1}{11}$

$\frac{111}{100}$

Explanation

To convert this decimal to a fraction, rewrite over .

$\frac{0.11}{1}$

In the numerator, move the decimal place in two places to the right. Then add two zeros after the one in the denominator.

$\frac{0.11}{1} = \frac{0.11}{1.00}= \frac{11}{100}$

The answer is $\frac{11}{100}$ .

What is the fractional equivalent of the sum ?

$\frac{11}{40}$

$\frac{9}{40}$

$\frac{275}{999}$

$\frac{225}{999}$

$\frac{21}{80}$

Explanation

First simplify .

Since has a decimal 3 places from the right, divide this number by , and move the numerator decimal 3 places to the right. As a result:

$0.275=\frac{275}{1000}$

This fraction can be reduced fully by using common factors. Simplify.

$\frac{275}{1000} = \frac{25 \cdot 11}{25 \cdot 40} = \frac{11}{40}$

Convert to a fraction.

$\frac{11}{100}$

$\frac{11}{10}$

$\frac{1}{9}$

$\frac{1}{11}$

$\frac{111}{100}$

Explanation

To convert this decimal to a fraction, rewrite over .

$\frac{0.11}{1}$

In the numerator, move the decimal place in two places to the right. Then add two zeros after the one in the denominator.

$\frac{0.11}{1} = \frac{0.11}{1.00}= \frac{11}{100}$

The answer is $\frac{11}{100}$ .

What fraction is ?

$\frac{9999}{10000}$

$\frac{9}{10}$

$\frac{8}{9}$

$\frac{1}{9}$

Explanation

Divide by one.

$\frac{0.9999}{1}$

Move the decimal place on the numerator 4 units to the right. Add as many zeros as placeholders for the denominator as many times as the decimal has moved. In other words multiply the numerator and denominator by 10000.

$\frac{0.9999\cdot 10000}{1 \cdot 10000}=\frac{9999}{10000}$