Although fractions can look intimidating, at their core, they are simply a division problem where the numerator is being divided by the denominator. Viewing it as such can make them seem less scary to deal with.
Once you make this mental switch, understanding how to convert fractions to decimals becomes much easier. Of course, you can just use a decimal calculator, but it's important to understand how to solve these problems with written methods.
There are two main methods by which these conversions are done. We’ll explain both in this article, along with examples to show them in practice.
Without further ado, let’s dive in!
You can convert fractions to decimals using the long division method and the power of 10 method. You may be familiar with the long division method. If so, conversions from any type of fraction – whether they are improper or proper fractions – should be a piece of cake. If not, don’t worry; we’ll talk you through how to do it.
Whilst all fractions can be done with the long division method, there are some that you’ll be able to do using the power of 10 method. It’s only reserved for fractions where the denominator can be multiplied into a power of 10. Since multiplying can be much simpler than dividing, it’s a useful method to have in your tool belt.
The most popular method to convert a fraction to a decimal number is by using the long division method.
The long division method is a tried and tested technique that has been in existence since around 1600. It was introduced to the world by an English mathematician named Henry Briggs.
So useful is the long division method that it can be utilized for any division problem, including if you want to convert a fraction to a decimal. All you need to do is divide the numerator by the denominator using the steps outlined, and you will find the answer.
To help you understand the concept of using long division, we’ll start with easy practice questions and then move on to some difficult ones.
But before we start, let’s brush up on some long division problem jargon:
- Dividend = the number that is being divided
- Divisor = the number that you are dividing the dividend by
- Quotient = located above the dividend; it is the final answer
Converting fractions to decimals: long division method example 1
Suppose you want to convert the improper fraction 1/2 into a decimal number.
Step 1: First, you want to identify the dividend and divisor. The numerator is your dividend, and the denominator is your divisor, which means 1 is the dividend and 2 is the divisor.
Step 2: Create a division bracket, with the divisor (2) on the left of it and the dividend (1) inside it. Now you can begin the long division process.
Step 3: 2 is bigger than 1 and cannot divide it directly. Therefore, you write 0 in the quotient above the 1 and also write 0 next to the 1 inside the division bracket to create the number 10. It’s important to also write the decimal point beside the quotient 0.
Step 4: You now have a new dividend which is 10. 10 is bigger than 2 and can thus be divided by it.
Step 5: Fortunately, 2 goes into 10 exactly 5 times. Therefore, you can write 5 next to the decimal point in the quotient to create 0.5.
Step 6: Since there are no more numbers in the dividend, you have finished the calculation and have reached the final answer.
Thus, 1/2 = 0.5
This was fairly straightforward since you probably know that 1/2 = 0.5. So let’s look at some harder fraction to decimal examples.
Converting fractions to decimals: long division method example 2
Suppose you want to convert 2/7 into a decimal number and calculate it to two decimal places. You can use the same steps as above to do so.
Step 1: First, identify the dividend and divisor. For this fraction, 2 is the dividend, and 7 is the divisor.
Step 2: Create a division bracket with 7 to the left of it and the 2 inside it. Now you can begin the long division process.
Step 3: 7 is bigger than 2, which means you cannot divide it directly. So, write 0 in the quotient and a 0 next to the dividend to create the number 20. Don’t forget to include the decimal point beside the quotient 0 as well.
Step 4: You now have a new dividend which is 20. 20 is bigger than 7 and can thus be divided by it.
Step 5: If you multiply 7 x 3 you get 21 which is too big. But, if you multiply 7 x 2 you get 14. 14 is smaller than 20, so you can use this calculation.
Step 6: Since you multiplied 7 by 2 to reach 14, you can write 2 next to the decimal point in the quotient. You can also write 14 below the dividend (20).
Step 7: Subtract 14 from 20, which gives you 6. This is the remainder and can be written below the 14 to give you your new dividend. Here, you can repeat steps 4-7 until you have no remainders.
Step 8: 6 is too small to be divided by 7. Therefore, you can write 0 next to the 6 to create 60. 60 is bigger than 7 and can thus be divided by it.
Step 9: 7 x 9 = 63 which is too big. But, if you multiply 7 x 8 you get 56. 56 is smaller than 60, so you can use this calculation.
Step 10: Since you multiplied 7 by 8, you can write 8 next to the 2 in the quotient and write 56 below the 60.
Step 11: Subtract 56 from 60, which gives you 4. This is the remainder and can be written below the 56 to give you your new dividend.
Step 12: 4 is too small to be divided by 7. Therefore, you can write 0 next to the 4 to give you 40. 40 can be divided by 7 and can thus be divided by it.
Step 13: 7 x 5 = 35. You cannot multiply 7 by 6 as this gives us 42. Therefore, you can write 5 next to the 8 in the quotient. Since you are calculating the answer to two decimal places, you can move on to rounding up.
Step 14: The quotient is 0.285. Since we are rounding up to two decimal places, the final answer is 0.29.
Thus, 2/7 = 0.29
As you can see, this math problem had many more steps compared to the first example. You will need to repeat steps 4-7 for as long as it takes to reach the final answer or until you can round up to the specified decimal place.
The power of 10 method is a nifty tool you can add to your arsenal when it comes to converting fractions to decimal numbers.
It’s a simple concept that involves changing the fraction’s denominator to a power of 10 – 10, 100, 1,000, 10,000, etc. This is done by finding which whole number you can multiply the denominator by to get a power of 10.
Then, both the numerator and the denominator must be multiplied by the whole number to create a new fraction.
Then, you simply have to divide the new numerator by the new denominator and ensure the decimal point is in the correct place value. And there you have it; you have reached your final answer.
It can sound a little confusing when explained, so let’s take a look at some examples to see it in action.
Converting fractions to decimals: multiplication method example 1
Suppose you have the fraction 3/5 and you want to show this in decimal form.
Step 1: First, you must determine what number you can multiply the denominator (5) by to make it into a power of 10.
Step 2: You know that 5 goes into 10 exactly twice (5 x 2 = 10), which means you can multiply 5 by 2 to give you 10 – the new denominator.
Step 3: Since you multiplied the denominator by 2, you must do the same to the numerator.
Step 4: 3 x 2 = 6. This is the new numerator.
Step 5: You now have a new fraction, which is 6/10.
Step 6: The next step is to divide 6 by 10. Another way to look at this is to move the place value of the numerator’s decimal point left, as many places as there are zeros in the denominator.
Step 7: 6 ÷ 10 = 0.6 This is the final answer.
Therefore, 3/5 = 0.6
Seems easy enough, right? Let’s take a look at a slightly more challenging example.
Converting fractions to decimals: multiplication method example 2
Suppose you have 23/40 and want to convert this fraction to its decimal equivalent. You can follow the same steps as above to reach the answer.
Step 1: First, you must determine what number you can multiply the denominator (40) by to change it into a power of 10.
Step 2: 40 cannot be multiplied into 100 by a whole number, but it can be multiplied into 1,000 by 25. Therefore, 1,000 becomes the new denominator.
Step 3: Since you multiplied the denominator by 25, you must do the same to the numerator.
Step 4: 23 x 25 = 575. This is the new numerator.
Step 5: You now have a new fraction, which is 575/1000.
Step 6: The next step is to divide 575 by 1000. Alternatively, you can move the place value of the numerator’s decimal point left, as many places as there are zeros in the denominator.
Step 7: Since there are three zeros in 1,000, you can move the decimal point three places to the left. This gives you the decimal value of 0.575, which is the final answer.
Therefore, 23/40 = 0.575
There are some common conversions that you should keep in mind as they’ll make your life a hell of a lot easier. As such, the following fraction to decimal chart can be a helpful framework for making quick and easy conversions on the spot.