# Decimal to Percent Converter

By Rita Rain
Last updated: Dec 04, 2020

The decimal to percent converter (A.K.A. the convert decimal to percentage calculator) lets you change (turn) a decimal value into a percentage. As it calculates in both directions, it can also serve as a percent to decimal converter.

Actually, it works just as well for whole numbers too - you can turn any number to percent!

Read the text below to learn how to convert decimal to percent, how to turn a number into a percent, and how to change percent to decimal on your own.

## What are decimals? - an introduction

The Hindu–Arabic numeral system (or Indo-Arabic numeral system) is a decimal positional system, nowadays the most commonly used numeral system in the world. Other systems include binary and hexadecimal systems.

Let's explain what it means. "Decimal" means the system is based on 10. "Positional notation" means we assign a different value to a symbol depending on its position. For example, the digit "3" in "13" equals 3, but in "342" it equals 300.

The system is much more practical than the alternatives, like representing numbers with lines (that's what some ancients would do). So, instead of having "|||||||||||||||" you just write "15". This way, using ten symbols (0-9), we can represent any rational number.

If we were to write a general formula for a 4-digit number, it could look like this:

`a₃a₂a₁a₀ = a₃*1,000 + a₂*100 + a₁*10 + a₀*1`

The symbol "a" here stands for a digit from 0 to 9. The index next to "a" denotes the digit's place (we count from 0, from right to left).

To get the number (right side of the equation), we multiply each digit by the powers of ten (1, 10, 100, ...). The indexes tell us how many zeros each of the powers of ten should have. If a digit is in the "zeroth" place, we multiply by 1, if its in the first place - by 10, in the second - 100, in the third - 1000, and so on.

We use the powers of ten to describe each position - the one's place, the ten's place, the hundred's place, and so on.

Take a look at a few examples:

`11 = 1*10 + 1*1`

`23 = 2*10 + 2*1`

`145 = 1*100 + 4*10 + 5`

`43210 = 4*10000 + 3*1000 + 2*100 + 1*10 + 0*1`

Now, what if you want to write down a decimal fraction?

To answer the problem we need to use a decimal point - a dot (or a comma) - to separate the whole numbers from the fractions.

`a₂a₁a₀.b₁b₂b₃ = a₂*100 + a₁*10 + a₀*1 + b₁/10 + b₂/100 + b₃/1000`

To the left of dot we multiply by ten, to the right - we divide by ten.

Examples:

`376.49 = 3*100 + 7*10 + 6 + 4/10 + 9/100`

`0.321 = 0*1 + 3/10 + 2/100 + 1/1000`

## What are percents? - an introduction

Percent means "out of a hundred" (from Latin) and represents a ratio or number as a fraction of 100. We denote it with the percent sign "%":

`1% = 1/100`

For example, 15% is equal to 15/100 and means "fifteen out of a hundred".

Examples:

• "40% of students in our school are female". The sentence implies that if the school has 100 students, 40 of them are girls.

• If you had a bowl with 100 corn flakes in it and you'd eaten 20%, you'd have eaten 20 out of 100, so 20 flakes.

But it's not like we only talk about percents when there's 100 of something. Percents represent a ratio. Let's go through another example:

• In a forest, 60% of trees are deciduous. 10,000 trees grow in the forest. How many deciduous trees are there?

Remember: `1% = 1 / 100`.

In this case: `60% = 60 / 100`.

Once we have the fraction form, we can transform it. We know we have 10,000 trees, so we need to change the denominator:

`60/100 = 60*100 / 100*100`

`60/100 = 6,000 / 10,000`

The denominator expresses the number of all the trees, and the numerator is the number of deciduous trees. Here is the answer - there are 6,000 leafy trees.

Both percents and decimals are common ways of representing fractions; let's learn how to convert between them.

## How to convert decimal to percent by hand?

This type of conversion is quite simple, so you should be able to do it without the decimal to percent calculator. You just need this formula:

`percent = decimal * 100`

To turn decimal to a percent, multiply the decimal by 100%.

## How to turn a decimal into a percent? - examples

Let's see how to turn a decimal into a percent in the below cases:

• `0.5 = 0.5 * 100%`

`0.5 = 50%`

• `0.37 = 0.37 * 100%`

`0.37 = 37%`

• `0.45372 = 0.45372 * 100%`

`0.45372 = 45.372%`

Notice all you need to do is move the decimal point two places to the right.

• `23.456 = 23.456 * 100%`

`23.456 = 2345.6%`

You can practice with other numbers and check your answers using the decimal to percentage converter.

## How to use the decimal to percent converter?

To use our convert decimal to percent calculator:

1. Input the decimal number you want to convert in the first field of the decimal to percentage calculator.

2. The decimal to percent converter will display the result below the field.

## How to convert percent to a decimal by hand?

To convert percent to decimal, simply divide by 100:

`decimal = percent / 100`

Let's say you've eaten 20% of a cake. To express this piece of cake as a decimal fraction, divide 20 by 100:

`20/100 = 0.2`

## How to turn a percent into a decimal? - examples

As always, a good bunch of examples will help you to understand how to turn a percent into a decimal:

• `40% = 40 / 100`

`40% = 0.4`

• `676% = 676 / 100`

`676% = 6.76`

• `0.022% = 0.022 / 100`

`0.022% = 0.00022`

Again, all we've done here is move the decimal point two places to the left.

Come up with your own examples and check your results by using this calculator as a percentage to decimal converter.

## Use our tool as a percentage to decimal converter

As we've mentioned many times before, you can use our calculator as a percentage to decimal converter:

1. Input the percentage first, in the second field of the percentage to decimal calculator.
2. You'll see the decimal equivalent in the first field.

That's it! You can use our calculator quickly in two ways.

## Turn a number to a percent and a percent to a number

Now we'll learn how to turn a number into a percent. Although the calculator is dedicated to decimals, you can use it to convert a number to percentage and vice versa. Any number, including whole numbers.

It works the same way - to turn a number into a percent, you need to multiply it by 100%. If you want to use the number to percent calculator, enter a number in the "decimal" field.

Let's have a look at examples of how to turn a number into a percent:

• Betty ran twice as far as John. What percentage of John's distance did Betty complete?

`b` will stand for Betty's distance, `j` for John's distance:

`b = 2 * j`

`b = 2 * (100% of j)`

`b = 200% of j`

Answer: Betty ran 200% of what John did.

• Catherine, `c`, earns half as much again as Josh, `j` (is it a gender paygap?). What percentage of Josh's pay does Catherine earn?

"Half as much again" means one whole plus a half, so:

`c = 1 * j + 0.5 * j = 1.5 * j`

`c = 1.5 * (100% of j) = 150% of j`

Answer: Catherine earns 150% of Josh's pay.

Now, let's perform a reverse operation - let's see how to turn a percent into a number.

All you need to do is divide the percentage by 100%:

• The tea consumed weekly by Anna, `a`, equals 400% of what Jennifer, `j`, drinks. If Jennifer drinks one cup per week, how many does Anna have?

'a = 400% of j`

`a = 400% of j / 100%`

`a = 4 * j`

if `j = 1`, then

`a = 4 * 1 = 4`

Answer: Anna drinks 4 cups of tea per week.

Rita Rain
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