Decimal to Percent Calculator

This calculator converts decimal values to percentages based on the fundamental assumption that 1 = 100%. The conversion is usually performed for values less than or equal to 1. However, the calculator can also be used for values greater than 1. Since any integer can be written as a decimal fraction, whole numbers can also be converted to percentages.

Directions for use

To use this decimal to percent converter, enter the given decimal, and press “Calculate.” The calculator will perform the decimal to percentage conversion, and return the final answer, as well as the detailed solution algorithm.

Use a dot to separate the whole number part from the fractional part, for example 3.5, 0.0076, 7.89. Both positive and negative numbers can be used as inputs. If you use an integer as an input, you don’t have to add a decimal point, i.e., you don’t have to enter 3.0; 3 is a valid input value.

Note that this calculator only converts decimals to percentages. Conversion of simple fractions is not possible.

Converting decimals to percents

Since the conversion is performed based on the fundamental assumption that 1 = 100%, to convert any decimal to percent, simply multiply the given number by 100%. Multiplication by 1 does not change the value of a number, therefore, multiplication by 100% = 1 will not change the value either.

Alternatively, this conversion can be visualized as shifting the decimal point 2 positions to the right. If the number does not have any significant digits left, add a zero for each shift of the decimal point position. Don’t forget to add the % sign at the end!

Example 1

Convert 0.76 to percentage.

Solution

Following the algorithm described above, to convert 0.76 to percentage, we simply have to multiply it by 100%:

0.76 × 100% = 76%

Using an alternative algorithm, we first need to shift the decimal point 2 places to the right, resulting in 76. And then add the % sign: 76%.

Answer

0.76 = 76%

Example 2

Convert 2.5 to percentage.

Solution

Following the algorithm described above, to convert 2.5 to percentage, we have to multiply it by 100%:

2.5 × 100% = 250%

Answer

2.5 = 250%

Note that the final value exceeds 100%. If 100% represents a “whole,” then exceeding that value means we are talking about several “wholes”. Let’s imagine a situation where the “whole” corresponds to a glass of water, then 100% is a full glass, while 50% corresponds to the situation when the glass is only half-full. 200% will correspond to 2 “wholes” or 2 glasses. And in the example above, 250% corresponds to 2.5 glasses of water.

Converting percents to decimals

To convert percents to decimals, the process described above is reversed. This means, that you have to divide the percentage value by 100% to get the decimal value. Similarly to the above process, since 1 = 100%, dividing by 100% does not change the given value.

Reversing the alternative process, to convert percents to decimals, shift the decimal point 2 positions to the left, and remove the % sign at the end. Also here, if the number doesn’t have any significant digits left, add a zero for each shift of the decimal point position.

Example 3

Convert 67.5% to a decimal.

Solution

To convert 67.5% to a decimal, we simply have to divide it by 100%:

67.5% / 100% = 0.675

Answer

67.5% = 0.675

Example 4

Convert 300% to a decimal.

Solution

To convert 300% to a decimal, we have to divide it by 100%:

300% / 100% = 3

Answer

300% = 3

Also here, note how the percentage value exceeds 100%, which corresponds to a number greater than 1. If we imagine a situation where 100%, or a “whole,” corresponds to an apple, then 300% corresponds to 3 apples.

Real life example

Discounts in shops

In shops the discounts are usually expressed in percentages. However, to calculate the final price you would need to perform the percent to decimal conversion. Let’s look at an example.

Sara is choosing a dress in a store. She found a nice dress with a 25% discount. The original price of the dress was $35. How much does the dress cost now that it’s on sale?

Solution

To calculate the final value of the dress, we will first need to calculate the dollar equivalent of the 25% discount, and then subtract it from the original price. The solution algorithm is presented below:

1. Find the value of the 25% discount, by converting 25% to a decimal and multiplying the original price by this decimal value.
2. Subtract the discount found in step 1 from the original price.

Following the algorithm, we get:

1. Converting 25% to a decimal:

25% = 25% / 100% = 0.25

Multiplying the original price by this decimal:

35 × 0.25 = 8.75

The dollar equivalent of the discount is $8.75

2. Subtracting the discount from the original price:

$35 - $8.75 = $26.25

Answer

The dress currently costs $26.25.