Decimal to Fraction Calculator

Decimal

Fraction

The decimal number (w/o repeating digits) Repeating digits (if any)

Please provide your input and click the calculate button

About the Decimal to Fraction Calculator

This right triangle calculator lets you calculate the length of the hypotenuse or a leg or the area of a right triangle. For each case, you may choose from different combinations of values to input.

Also, the calculator will give you not just the answer, but also a step by step solution. So you can use it as a great tool to learn about right triangles.

Usage Guide

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i. Valid Inputs

Depending on the type of calculator you choose (using the the drop-downs), you'll will need to enter a fraction, a decimal, or a percentage value. Here are the valid inputs for each of those types.

Fractions — When providing an input in the "fraction" field, you may enter a number in one of the following formats.

Integers → $\hspace{0.2em} 2 \hspace{0.2em}$ , $\hspace{0.2em} 0 \hspace{0.2em}$ , $\hspace{0.2em} -4 \hspace{0.2em}$
Fractions → $\hspace{0.2em} 2/3 \hspace{0.2em}$ , $\hspace{0.2em} -1/5 \hspace{0.2em}$
Mixed numbers → $\hspace{0.2em} 5 \hspace{0.4em} 1/4 \hspace{0.2em}$

Percentage — In addition to the inputs accepted for a "fraction", you can also enter a decimal number when providing a "percentage" input. For example, $\hspace{0.2em} 12.75 \hspace{0.2em}$ .

Decimals — If your input is a terminating decimal, enter the whole thing in the first field.

For recurring decimals, enter everything except the recurring part into the first field. And then, enter the recurring digits into the second field.

For example, if you had to enter $\hspace{0.2em} 4.15\overline{72} \hspace{0.2em}$ , you'd enter $\hspace{0.2em} 4.15 \hspace{0.2em}$ in the first input box and $\hspace{0.2em} 72 \hspace{0.2em}$ in the second.

ii. Example

If you would like to see an example of the calculator's working, just click the "example" button.

iii. Solutions

As mentioned earlier, the calculator won't just tell you the answer but also the steps you can follow to do the calculation yourself. The "show/hide solution" button would be available to you after the calculator has processed your input.

iv. Share

We would love to see you share our calculators with your family, friends, or anyone else who might find it useful.

By checking the "include calculation" checkbox, you can share your calculation as well.

Here's a quick overview of how to convert decimals to fractions.

For those interested, we have a more comprehensive tutorial on how to convert decimals into fractions.

Converting Decimals into Fractions

First things first.

You can convert a decimal into a simple fraction (fractions in which both top and bottom numbers are integers) if and only if the decimal number is terminating or repeating.

Non-terminating non-repeating decimals cannot be converted into simple fractions.

Terminating Decimals into Fractions

To convert a decimal into a fraction

Count the number of digits on the right of the decimal point. Let's call it $\hspace{0.2em} n \hspace{0.2em}$
Multiply and divide the number by $\hspace{0.2em} 10^n \hspace{0.2em}$
Simplify the resulting fraction.

Here's an example to help you understand.

Example

Convert $\hspace{0.2em} 1.25 \hspace{0.2em}$ into a fraction.

Solution

Alright, we'll be following the steps outlined above.

There are $\hspace{0.2em} {\color{Red} 2} \hspace{0.2em}$ digits to the right of the decimal point. So we multiply and divide the number by $\hspace{0.2em} 10^ {\color{Red} 2} \hspace{0.2em}$ .

\begin{align*} 1.25 \hspace{0.25em} &= \hspace{0.25em} \frac{1.25 \times 10^2}{10^2} \\[1.5em] &= \hspace{0.25em} \frac{125}{100} \end{align*}

Finally, simplifying the fraction, we have

\frac{125}{100} \hspace{0.25em} = \hspace{0.25em} \frac{5}{4}

So, $\hspace{0.2em} 1.25 \hspace{0.2em}$ expressed as a fraction is $\hspace{0.2em} 5 / 4 \hspace{0.2em}$ .

Repeating Decimals into Fractions

Let me use the following example to explain how we convert repeating decimals to fractions.

Example

Convert

\hspace{0.2em} 0.3\overline{15} \hspace{0.2em}

into a fraction.

Solution

Step 1. Assign the decimal number to some variable, say $\hspace{0.2em} x \hspace{0.2em}$ .

x \hspace{0.25em} = \hspace{0.25em} 0.3\overline{15}

Step 2. Multiply the number by a suitable power of $\hspace{0.2em} 10 \hspace{0.2em}$ such that the non-repeating decimal digits move to the left of the decimal point.

Here, we have one non-repeating decimal digit. Multiplying the number by $\hspace{0.2em} 10 \hspace{0.2em}$ will do the job for us.

\begin{align*} 10x \hspace{0.25em} &= \hspace{0.25em} 10 \times 0.3\overline{15} \\[1em] 10x \hspace{0.25em} &= \hspace{0.25em} 3.\overline{15} \hspace{0.25cm} \rule[0.1cm]{1cm}{0.1em} \hspace{0.15cm} (1) \end{align*}

Step 3. Multiply the number by a suitable power of $\hspace{0.2em} 10 \hspace{0.2em}$ such that one set of repeating decimal digits also move to the left of the decimal point.

Here, we have $\hspace{0.2em} 1 \hspace{0.2em}$ non-repeating decimal digit and $\hspace{0.2em} 2 \hspace{0.2em}$ repeating digits. Multiplying the number by $\hspace{0.2em} 10^3 \hspace{0.2em}$ (or $\hspace{0.2em} 1000 \hspace{0.2em}$ ) will move the $\hspace{0.2em} 3 \hspace{0.2em}$ digits to the left of the decimal point.

\begin{align*} 1000x \hspace{0.25em} &= \hspace{0.25em} 1000 \times 0.3\overline{15} \\[1em] 1000x \hspace{0.25em} &= \hspace{0.25em} 315.\overline{15} \hspace{0.25cm} \rule[0.1cm]{1cm}{0.1em} \hspace{0.15cm} (2) \end{align*}

Wondering how we have $\hspace{0.2em} .\overline{15} \hspace{0.2em}$ after the decimal point, even after moving those digits to the left? Remember, those are repeating digits. So $\hspace{0.2em} 0.3\overline{15} \hspace{0.2em}$ is the same as $\hspace{0.2em} 0.3151515... \hspace{0.2em}$ .

Step 4. Subtract equation $\hspace{0.2em} 1 \hspace{0.2em}$ from $\hspace{0.2em} 2 \hspace{0.2em}$ and solve from $\hspace{0.2em} x \hspace{0.2em}$ .

So,

	$\hspace{0.2em} 1000x \hspace{0.2em}$	$\hspace{0.2em} = \hspace{0.2em}$	$315$	$.\overline{15}$
$-$	$\hspace{0.2em} 10x \hspace{0.2em}$	$\hspace{0.2em} = \hspace{0.2em}$	$3$	$.\overline{15}$
	$\hspace{0.2em} 990x \hspace{0.2em}$	$\hspace{0.2em} = \hspace{0.2em}$	$312$	$.00$

Dividing both sides by $\hspace{0.2em} 990 \hspace{0.2em}$ , we have

\begin{align*} x \hspace{0.25em} &= \hspace{0.25em} \frac{312}{990} \\[1.5em] &= \hspace{0.25em} \frac{52}{165} \end{align*}

That's it. $\hspace{0.2em} 0.3\overline{15} \hspace{0.2em}$ expessed as a fraction is $\hspace{0.2em} 52/165 \hspace{0.2em}$ .