How to Compare Fractions? A Kid-Friendly Guide
Check out our elementary-school-friendly guide on comparing fractions with easy-to-follow definitions and guide, solved examples, and exercises for practice.
Decimals and fractions are two different ways, or formats, to express quantities. You can think of them as two sides of the same coin!
Whether you’re following a recipe that calls for \( \Large \frac{1}{2}\) liter of milk or 0.75 cup of sugar, or you are measuring lengths such as 1.5 meters or 1\( \Large \frac{2}{3}\) yards, you will see these formats used almost interchangeably.
But, how do you keep track of fractions and decimals when they appear in the same recipe, for example?
It’s simple! We convert all values into the same format.
In this guide, you’ll find easy-to-follow steps to converting fractions to decimals (and vice versa) with simple definitions, solved examples, and a practice test.
Enjoy!
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Fractions and decimals are ways to represent parts of a whole or parts of whole numbers.
A fraction is a way to show a part of something by dividing it into equal pieces. It has two parts:
For example, in the fraction \( \Large \frac{3}{4}\), the numerator is 3 indicates that we have 3 parts of a whole which consists of 4 parts, as indicated by denominator.
A decimal is another way to represent fractions but based on powers of 10. Decimals use a decimal point to separate the whole number from the fractional part.
For example, the fraction \( \Large \frac{1}{2}\) can also be written as the decimal 0.5.
Here: 0 is the whole number part, while .5 is the decimal part.
Decimals are especially useful in calculations and measurements as they are often easier to add, subtract, multiply, and divide than fractions.
Both fractions and decimals give us a flexible way to work with numbers that aren't whole.
There are two main methods you can use to convert fractions to decimals:
The most commonly used method to convert a fraction to decimal without a calculator is long division.
To do this, remember the steps you learned from long division:
Let’s follow these steps to convert \( \Large \frac{3}{4}\) to a decimal.
Step 1: Set Up the Division Task
Set up the fraction as a division problem, with 3 (numerator) as the dividend and 4 (denominator) as the divisor.
Step 2: Add a Decimal Point
Our divisor 4 is smaller than the dividend 3 which means that the number of times it goes into it is 0.
Add 0. to your quotient.
Then, add a .0 after the dividend: 3.0.
To make the next step easier, we will represent the dividend 3.0 as 30.
Step 3: Divide
Check how many times 4 goes into 30.
Since 30 isn’t divisible by 4, we can find the number closest to 30 that’s divisible by 4 which is 28.
28÷4=7
We see that 4 goes into 30 a total of 7 times.
Write 7 after the decimal above the division bar.
Step 4: Multiply
Now multiply 7 by the divisor (4).
7×4=28
Write 28 below the dividend.
Step 5: Subtract
Subtract 28 from 30 and write the result below.
30−28=2
Step 6: Bring Down
Since 4 (the divisor) can’t fit into 2, we add another zero to the dividend to make it 3.00.
Then we bring the zero down, next to 2 and make it 20.
Step 7: Divide Again
Check how many times 4 goes into 20.
20÷4=5
This shows us that 4 fits into 20 a total of 5 times.
Write 5 next to 7 in the quotient above the division bar.
Step 8: Multiply Again
Multiply 5 by 4 and write the result below.
5×4=20
Step 9: Final Subtraction
Subtract 20 from 20.
20−20=0
Since there is no remainder, we will stop here.
The final answer is: \( \Large \frac{3}{4}\) = 0.75
Another method to convert fractions to decimals is to change the denominator to a power of 10, such as 10, 100, or 1,000.
Note that this method only works for fractions where the denominator can be adjusted to reach a power of 10.
Let's use this method to convert \( \Large \frac{3}{5}\) to a decimal:
Step 1: Find the Multiplier
Find what number to multiply the denominator 5 by to reach the closest power of 10.
This would be:
5×2=10
So, our multiplier is 2.
Step 2: Multiply the Fraction
Now, multiply the denominator and the numerator by this number (2).
\( \Large \frac{3x2}{5x2}\)=\( \Large \frac{6}{4}\)
Step 3: Convert the New Fraction to a Decimal
Now, we have a new fraction, \( \Large \frac{6}{10}\), we can convert it to a decimal.
We check how many zeroes the denominator has. Since 10 has one zero, we place the decimal one place to the left.
So, \( \Large \frac{6}{10}\) becomes 0.6.
Similarly, if the denominator had two zeros, we would get 0.06. If it had four zeros, we would get 0.0006 and so on.
Could we apply this method to a fraction like \( \Large \frac{2}{3}\)
No, because the denominator 3 cannot be adjusted to reach a power of 10.
Converting decimals into fractions is usually simpler than the other way around. The logic is simple:
Let’s convert 0.7 into a fraction.
Step 1: Find Where the Decimal Ends
First, look at where the decimal ends.
In our case, 0.7 ends in the tenths place.
Step 2: Make the Fraction
The place where the decimal ends becomes your denominator.
Since our decimal ends in the tenths, our denominator will be 10.
The digit behind the decimal point and zeros (if any) becomes your numerator.
So, by converting 0.7 into a fraction, we get: \( \Large \frac{7}{10}\).
Step 3: Simplify if Necessary
Finally, check if the fraction can be simplified.
In this case, \( \Large \frac{7}{10}\) is already in its simplest form!
When a decimal has both a whole number and a fractional part (e.g. 1.25, 2.5, 3.2, and so on), the principle of conversion remains the same, with one additional step.
Let’s try to convert 1.66 into a fraction.
Step 1: Separate the Whole Number and Decimal
For 1.66, the whole number is 1, and the decimal is 0.66.
Step 2: Find Where the Decimal Ends
Check where the decimal ends.
In this case, 0.66 ends in the hundredths.
Step 3: Make the Fraction
The place where the decimal ends becomes your denominator.
Since 0.66 ends in the hundredths, the denominator is 100.
The digit behind the decimal becomes the numerator. In this case, it’s 66.
So, we will have \( \Large \frac{66}{100}\).
Step 4: Simplify if Necessary
Finally, check if the fraction can be simplified.
In this case, both 66 and 100 are divisible by 2.
\( \Large \frac{66÷2}{100÷2}\)=\( \Large \frac{33}{50}\)
Finally, the decimal 1.66 is equivalent to the mixed number 1 \( \Large \frac{33}{50}\)
Let’s see a few more examples that illustrate how converting decimals and fractions works.
Let's convert \( \Large \frac{2}{3}\) using the long division method.
Step 1: Set Up the Division Task
Set up the fraction as a division problem, with 2 (numerator) as the dividend and 8 (denominator) as the divisor.
Step 2: Add a Decimal Point
Since 8 can’t go into 2, place a 0 and a decimal point in the quotient.
Place a decimal point after 2 (the dividend) and add a zero to make it 2.0. We will now treat the dividend as 20 for easier calculations.
Step 3: Divide
Check how many times 8 goes into 20.
Since 20 isn't divisible by 8, let's find the number closest to 20 that is divisible by 8. That number is 16.
16÷8=2
So, 8 goes into 20 a total of 2 times. We place the 2 above the division bar in the quotient, right after the decimal point.
Step 4: Multiply
Now multiply 2 by the divisor (8).
2×8=16
Write 16 below the dividend.
Step 5: Subtract
Subtract 16 from 20.
20−16=4
Write the result below.
Step 6: Bring Down
Since 8 cannot go into 4, add another zero to the dividend (2.00) and bring it down next to 4.
Step 7: Divide Again
Check how many times 8 goes into 40.
40÷8=5
Write 5 next to 2 in the quotient.
Step 8: Multiply Again
Multiply 5 by 8 and write the result below.
5×8=40
Step 9: Final Subtraction
Subtract 40 from 40.
40−40=0
Write the result below.
Since there is no remainder, we will stop here.
The final answer is:
\( \Large \frac{2}{8}\)=0.25
Convert to a decimal using the denominator conversion method.
Step 1: Find the Multiplier
Find what number to multiply the denominator (8) by to reach the closest power of 10.
This would be:
8×125=1000
Step 2: Multiply the Fraction
Now, multiply the denominator and the numerator by the same number (125).
\( \Large \frac{5x125}{8x125}\)=\( \Large \frac{625}{1000}\)
Step 3: Convert the New Fraction to a Decimal
Check how many zeroes the denominator has. Since 1,000 has three zeroes, we place the decimal three places to the left.
\( \Large \frac{625}{1000}\)=0.625
So, \( \Large \frac{5}{8}\) converts to 0.625.
Convert the decimal 0.025 to a fraction.
Step 1: Find Where the Decimal Ends
With three digits after the decimal point, 0.025 ends in the thousandths place.
Step 2: Make the Fraction
The place where the decimal ends becomes the denominator.
Since 0.025 ends in the thousandths, the denominator will be 1,000.
The digits behind the decimal become the numerator. In this case, it’s 25.
Put the two together and our fraction is \( \Large \frac{25}{1000}\).
Step 3: Simplify Fraction
Check if the fraction can be simplified.
Both the numerator (25) and the denominator (1,000) are divisible by 25.
\( \Large \frac{25÷25}{1000÷25}\) =\( \Large \frac{1}{4}\)
0.025=\( \Large \frac{1}{40}\)
Let’s convert a decimal that consists of a whole number:
4.85
Step 1: Separate the Whole Number and the Decimal
First, separate the whole number from the decimal.
In this case, 4 is the whole number, and 0.85 is the decimal part.
Step 2: Find Where the Decimal Ends
The decimal 4.85 has two digits after the decimal point, so it ends in the hundredths place.
Step 3: Make the Fraction
The place where the decimal ends becomes the denominator. In this case it is 100.
The digits behind the decimal become the numerator. In this case, it’s 85.
So, the fraction will be \( \Large \frac{85}{100}\).
Step 4: Simplify If Necessary
Next, simplify \( \Large \frac{85}{100}\). Both numbers are divisible by 5.
\( \Large \frac{85÷5}{100÷5}\)=\( \Large \frac{17}{20}\)
We bring the whole number and the fraction together to form a mixed number: 4\( \Large \frac{17}{20}\).
It’s your turn!
Try these practice examples on your own and scroll to the end of the guide to check your answers.
Convert the fraction \( \Large \frac{4}{5}\) to a decimal using the long division method.
Convert the fraction \( \Large \frac{1}{8}\) to a decimal using the denominator conversion method.
Convert the decimal 0.035 to a fraction.
Convert the decimal 7.45 to a fraction.
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If you have given our exercises a go, check your answers here:
Exercise 1: 0.8
Exercise 2: 0.125
Exercise 3: \( \Large \frac{7}{200}\)
Exercise 4: 7\( \Large \frac{9}{20}\)