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Converting Between Decimals and Percents

Saying something is $67$% full is essentially the same as saying that if that thing could hold $100$ objects, it would only have $67$ objects in it. In other words, it's $67$ hundredths full. Multiplying the decimal form by $100$ gives the percentage! Just remember to add the $\%$ sign to the end of your answer.

If you remember how place value works for decimals, you know that the hundredths place is two digits to the right of the decimal point. The hundredths place is named that way because if you divide $1$ by $100$, you will get a $1$ in that place ($1 \div 100 = 0.01$).

Going from Percentage to a Decimal

So if you want to make $67$% into an equivalent decimal, all you have to do is divide by $100$. That way, the digit in the ones place for the percentage ($7$) will then be in the hundredths place for the decimal

$82$% $=0.82$, because $82 \div 100 =0 .82$.

This technique will also work if your percentage is OVER $100$% or if your percentage has a decimal itself. For example, $342.98$% is equal to $3.4298$ as a decimal. Notice we move the decimal point to the left two places.

Going from decimal to percent

If you want to go from decimal to percent, just do the reverse! Multiply your decimal by $100$, and you'll get a number that works as a percentage (this time, you're taking the number that's in the hundredths place and turning it into a number that goes in the ones place).

$0.72= 72$% because $0.72 \times 100 = 72$.

Just like for taking percentages to decimals, this technique will still work if your decimal is over $1$ or is more than two digits long.

Here is a graphic summarizing how to convert between a decimal and a percent, this time with $0.55$ and $55\%:$

(Video) Converting Decimals, Percents, and Fractions

by mathman1024

Here's a video by mathman1024 showing you how to convert between decimals, fractions, and percents. In this explanation we'll focus on decimals and percents. However, you can learn more about converting between decimals and fractions, or between percents and fractions.

Decimal $\rightarrow$ Percent

To go from a decimal to a percent, all you have to do is move the decimal point over to the right by two places. Tack on a percent sign and you're good to go.

For example, if we have $0.34$, we just move the decimal point to the right two spaces. This gives us $34$ and if we add on the percent sign we get our answer: $34\%$.

Percent $\rightarrow$ Decimal

When going from a percent to a decimal, just remove the percent sign and then move the decimal two places to the left.

For example, if we have $68\%$, we just need to remove the the percent sign, $68$, and then move the decimal two places to the left: $0.68$

Percent $\rightarrow$ Fraction

Going from a percent to a fraction is very easy.

1. Remove percent sign.
2. Put the number over $100$.
3. Reduce.

If we look at $68\%$ again: $$\begin{align} &\quad\quad\quad68\%\\ \hline &(1)\quad68\\ &(2)\quad\frac{68}{100}\\ &(3)\quad=\frac{34}{50}=\frac{17}{25} \end{align}$$ So, $68\%=\frac{17}{25}$.

(Video) How to Convert Percents to Decimals

by Mahalo Math

This video by Mahalo Math explains how to convert a percent to a decimal.

$\large{\text{Summary}}$

Converting a decimal to a percent is exactly the same thing just in the opposite direction. So since you move the decimal point over two places to the left when changing from a percent to a decimal, going from a decimal to a percent you will move the decimal point over two places to the right.

Example 1

Suppose you want to convert $55\%$ into a decimal. For converting a percentage to a decimal, move the decimal point two places to the left. $$55.\rightarrow5.5\rightarrow.55$$ Thus, our conversion is: $$55\%=0.55$$

Example 2

Suppose you want to convert $0.00782$ into a percent. To convert from decimal to percent, we move the decimal point two places to the right. $$0.00782\rightarrow00.0782\rightarrow000.782$$ Adding the percent sign, our conversion becomes: $$0.00782=0.782\%$$