Converting Fractions, Decimals, and Percentages
Master the art of switching between three different ways to write the same number.
Fractions, decimals, and percentages are three different languages for the same number. Mastering how to translate between them allows you to compare values easily and solve real-world problems involving money, grades, and discounts.
Have you ever wondered if getting $$[[frac{18}{20}]]$$ on a test is better than getting 85%? Or if a 0.5 discount is the same as half price? To answer these questions, we need to know how to convert between these three forms. They all represent parts of a whole, but they look different on paper.
From Fractions to Decimals and Percentages 🎯
A fraction is simply a division problem waiting to happen. To turn a fraction into a decimal, you divide the numerator (top number) by the denominator (bottom number).
Example: Convert $$[[frac{3}{8}]]$$
Perform the division $$3 [[div]] 8$$ to find the decimal value:
$$3 [[div]] 8 = 0.375$$
Once you have the decimal, converting to a percentage is straightforward. You simply multiply the decimal by 100 and add the “%” symbol:
$$0.375 [[times]] 100 = 37.5\%$$
Some fractions result in repeating decimals. For example, $$[[frac{1}{3}]]$$ becomes $$0.333…$$ which we write as $$33.3\%$$ (often rounded to one decimal place).
From Decimals to Percentages and Fractions 🔢
Decimals are often the easiest starting point. To convert a decimal to a percentage, you multiply by 100. This is the same as moving the decimal point two places to the right.
$$0.62 [[times]] 100 = 62\%$$
To convert a decimal to a fraction, you must look at the place value of the last digit. If the decimal is 0.6, the 6 is in the tenths place, so the fraction is $[[frac{6}{10}]]$. If the decimal is 0.25, it ends in the hundredths place, so the fraction is $[[frac{25}{100}]]$.
Example: Convert 0.45 to a Fraction
Write the number over its place value (hundredths):
$$0.45 = [[frac{45}{100}]]$$
Now, simplify the fraction by dividing the top and bottom by the Highest Common Factor (HCF), which is 5:
$$[[frac{45 [[div]] 5}{100 [[div]] 5}]] = [[frac{9}{20}]]$$
From Percentages to Fractions and Decimals âš¡
The word “percent” comes from “per centum,” which literally means “out of 100”. This definition gives us a direct path to creating a fraction.
To write a percentage as a fraction, place the number over 100 and remove the % sign. Then simplify if possible.
$$20\% = [[frac{20}{100}]] = [[frac{1}{5}]]$$
To write a percentage as a decimal, you do the opposite of what we did earlier. Divide the number by 100, which moves the decimal point two places to the left.
Example: Convert 150%
As a fraction:
$$150\% = [[frac{150}{100}]]$$
Simplify by dividing by 50:
$[[frac{3}{2}]]$ (or $1 [[frac{1}{2}]]$)
As a decimal:
$$150 [[div]] 100 = 1.5$$
Remembering these connections helps you check your work. If you calculate that $[[frac{1}{2}]] = 500\%$, you can quickly realize the error because $[[frac{1}{2}]] = 0.5$, which is only $50\%$.
Practice Problems
Test your conversion skills with these practice problems. Try to solve them before checking the answers.
1. Convert $[[frac{3}{5}]] $ to a percentage.
Check Answer
First, convert the fraction to a decimal by dividing 3 by 5:
$$3 [[div]] 5 = 0.6$$
Next, multiply by 100 to get the percentage:
$$0.6 [[times]] 100 = 60%$$
2. Convert 0.12 to a simplified fraction.
Check Answer
The decimal ends in the hundredths place, so write it over 100:
$$0.12 = [[frac{12}{100}]]$$
Find the HCF of 12 and 100, which is 4. Divide both numbers by 4:
$$[[frac{12 [[div]] 4}{100 [[div]] 4}]] = [[frac{3}{25}]]$$
3. Convert 8% to a decimal.
Check Answer
To convert a percentage to a decimal, divide by 100:
$$8 [[div]] 100 = 0.08$$
Interactive Quiz
Ready to prove your skills? Take this quick quiz to see how well you can convert between forms.