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ACT Math : How to find the fractional equivalent of a decimal

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Example Questions

Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

What is 0.48x $\displaystyle 0.48x$ equivalent to?

Possible Answers:

$\frac{24}{48}x$ $\displaystyle \frac{24}{48}x$

$\frac{24}{50}x$ $\displaystyle \frac{24}{50}x$

$\frac{48}{x}$ $\displaystyle \frac{48}{x}$

$\frac{24}{100}x$ $\displaystyle \frac{24}{100}x$

48x $\displaystyle 48x$

Correct answer:

$\frac{24}{50}x$ $\displaystyle \frac{24}{50}x$

Explanation:

We need to convert 0.48 $\displaystyle 0.48$ into a fraction.

To do this, write down $\frac{0.48}{1}$ $\displaystyle \frac{0.48}{1}$

Now, because the decimal goes to the hundreth place, multiply the numerator and denominator of the fraction by 100.

$\frac{0.48\times100}{1\times100}=\frac{48}{100}$ $\displaystyle \frac{0.48\times100}{1\times100}=\frac{48}{100}$

Now, simplify the fraction.

$\frac{48}{100}=\frac{24}{50}$ $\displaystyle \frac{48}{100}=\frac{24}{50}$

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Example Question #2 : Decimals

A tub of food contains 0.5 $\displaystyle 0.5$ pounds of vegetables, 1.75 $\displaystyle 1.75$ pounds of lard, and $\displaystyle 15$ pounds of sausage. What is its total weight as an improper fraction?

Possible Answers:

$\frac{17}{4}$ $\displaystyle \frac{17}{4}$

$\frac{91}{8}$ $\displaystyle \frac{91}{8}$

$\frac{18}{4}$ $\displaystyle \frac{18}{4}$

$\frac{83}{4}$ $\displaystyle \frac{83}{4}$

$\frac{69}{4}$ $\displaystyle \frac{69}{4}$

Correct answer:

$\frac{69}{4}$ $\displaystyle \frac{69}{4}$

Explanation:

To begin with, it is easiest just to add these decimals together using your calculator:

$\displaystyle 0.5+1.75+15=17.25$

Now, this is the same thing as:

$\displaystyle 17 + 0.25$

We can rewrite this:

$17 + \frac{1}{4}$ $\displaystyle 17 + \frac{1}{4}$

To find this, you need to give the two numbers a common denominator:

$17 + \frac{1}{4} = \frac{68}{4}+\frac{1}{4}=\frac{69}{4}$ $\displaystyle 17 + \frac{1}{4} = \frac{68}{4}+\frac{1}{4}=\frac{69}{4}$

This is your answer.

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Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

What is the fractional equivalent of 0.33 $\displaystyle 0.33$?

Possible Answers:

$\frac{3}{10}$ $\displaystyle \frac{3}{10}$

$\frac{33}{100}$ $\displaystyle \frac{33}{100}$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\frac{333}{1000}$ $\displaystyle \frac{333}{1000}$

Correct answer:

$\frac{33}{100}$ $\displaystyle \frac{33}{100}$

Explanation:

In decimal form 0.33 $\displaystyle 0.33$ is said 33 hundredths.

This is equal to

$\frac{33}{100}$ $\displaystyle \frac{33}{100}$.

This fraction cannot be reduced any further therefore it is in its final answer form.

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Example Question #2 : Decimals With Fractions

Write 0.45 as a fraction.

Possible Answers:

$\frac{11}{20}$ $\displaystyle \frac{11}{20}$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

$\frac{5}{9}$ $\displaystyle \frac{5}{9}$

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

$\frac{9}{20}$ $\displaystyle \frac{9}{20}$

Correct answer:

$\frac{9}{20}$ $\displaystyle \frac{9}{20}$

Explanation:

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

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

$\frac{9}{20}$ $\displaystyle \frac{9}{20}$

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Example Question #11 : Decimals

Convert this decimal to a fraction in reduced form:

$\large 0.3\overline{6}$ $\displaystyle \large 0.3\overline{6}$

Possible Answers:

$\frac{9}{25}$ $\displaystyle \frac{9}{25}$

$\frac{12}{37}$ $\displaystyle \frac{12}{37}$

$\frac{11}{30}$ $\displaystyle \frac{11}{30}$

$\frac{4}{11}$ $\displaystyle \frac{4}{11}$

Correct answer:

$\frac{11}{30}$ $\displaystyle \frac{11}{30}$

Explanation:

To figure out what fraction this decimal corresponds to, we have to get rid of the repeating part, otherwise we would be dealing with an infinite recursion and we don't have the tools to deal with that yet. Instead, we will set the decimal equal to $\displaystyle x$ and multiply it by 10, and also multiply it by 100.

$x = 0.3\overline{6}{}$ $\displaystyle x = 0.3\overline{6}{}$

$10x=3.\overline{6}{}$ $\displaystyle 10x=3.\overline{6}{}$

$100x = 36.\overline{6}{}$ $\displaystyle 100x = 36.\overline{6}{}$

Notice that in 10x $\displaystyle 10x$ and 100x $\displaystyle 100x$ we have the same repeating decimal part. So if we subtract them, it disappears:

$\displaystyle 100x-10x=33.0{}$

Now all that remains is to do the algebra.

$\displaystyle 90x=33{}$

$x=\frac{33}{90} = \frac{11}{30}{}$ $\displaystyle x=\frac{33}{90} = \frac{11}{30}{}$

$\frac{11}{30}{}$ $\displaystyle \frac{11}{30}{}$ is our final answer.

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Example Question #11 : Decimals

What is the fractional equivalent of 3.14 $\displaystyle 3.14$?

Possible Answers:

$\textup{None of these}$ $\displaystyle \textup{None of these}$

$\frac{71}{23}$ $\displaystyle \frac{71}{23}$

$\frac{157}{50}$ $\displaystyle \frac{157}{50}$

$\frac{51}{16}$ $\displaystyle \frac{51}{16}$

$\frac{22}{7}$ $\displaystyle \frac{22}{7}$

Correct answer:

$\frac{157}{50}$ $\displaystyle \frac{157}{50}$

Explanation:

To find the fractional equivalent of a decimal, set the decimal as a fraction over $\displaystyle 1$, then multiply top and bottom by one power of $\displaystyle 10$ for each digit after the decimal. In this case, we have two digits after the decimal, so we multiply top and bottom by 100 $\displaystyle 100$:

$3.14 = \frac{3.14}{1} = \frac{314}{100}$ $\displaystyle 3.14 = \frac{3.14}{1} = \frac{314}{100}$

Now, start simplifying.

$\frac{314}{100} = \frac{157}{50}$ $\displaystyle \frac{314}{100} = \frac{157}{50}$

Since we cannot reduce further, $3.14 = \frac{157}{50}$ $\displaystyle 3.14 = \frac{157}{50}$.

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ACT Math : How to find the fractional equivalent of a decimal

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

Example Question #2 : Decimals

Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

Example Question #2 : Decimals With Fractions

Example Question #11 : Decimals

Example Question #11 : Decimals

All ACT Math Resources

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