Converting between fractions, decimals, and percentages

Our first unit of work will deal with decimals, percentages, and rates and ratios. To start with we will look at how to convert between fractions, decimals, and percentages. These are essential skills, so make sure you know how do do all of the following. If you do need help with this, please feel free to comment on this post, or email or chat with me in person. 

Converting percentage to decimals

This is quite easy. All you really need to do is to divide the original percentage by 100 and you have your decimal.

For example: 47% to a decimal. All you would do is divide 47 by 100, giving you an answer of 0.47

Converting decimal to percentage

Again, this is quite easy. All we need to do is multiply the original decimal by 100 and you have your percentage.

For example: 0.82 to a percentage. Simply multiply 0.82 by 100, giving you an answer of 82%

Converting fractions to decimals

This is also quite simple. All that needs to be done is dividing the numerator by the denominator.

For example: 3/8 to a decimal. Divide 3 by 8, and you get 0.375, which is your answer.

Converting decimals to fractions

This is slightly more difficult. It involves a few steps. First, we need to make a fraction with the original decimal as the numerator, and the number 1 as the denominator. Once we have done this, we need to convert this decimal to a whole number by multiplying by a multiple of 10 (i.e. 10, 100, 1000, 10000, etc). We then need to multiply our denominator, 1, by this same factor of 10. Once we have done all of this, we simplify our fraction. Hopefully a few examples will help make sense of this.

Example 1:

 Example 2:

Converting percentages to fractions

This is much simpler than converting the decimals to fractions. Since we know that a percentage is a part out of 100, all we need to do is to make a fraction with the percentage as the numerator and 100 as the denominator. You then need to simplify your fraction.

For example: 36% as a fraction. Set up your fraction with 36 as the numerator and 100 as the denominator. You should get 36/100. Now simplify to get 9/25

Converting fractions to percentages

This is quite simple, as long as you have followed the skills I have gone thru above. The first thing you will need to do is to convert your fraction to a decimal, by dividing the numerator by the denominator. You then want to convert this decimal to a percentage by multiplying by 100.

For example: 6/20 as a percentage. First convert it to a decimal by dividing the numerator (6) by the denominator (20). You should get an answer of 0.3. You then want to convert this to a percentage by multiplying by 100. This will give you a final answer of 30%

Now in this post, and more specifically when I talk about fractions, I am talking about simplifying fractions. Now this should have been covered last year, but briefly it is basically finding a number that both the numerator and denominator of the fraction can be divided by, and then going out and actually dividing them by this number. This should keep the overall value of your fraction the same, but the numbers will be a little smaller. For example, if I had 2/6 as a fraction, both the numerator (2) and the denominator (6) can be divided by 2 to give a whole number as an answer. So if we divide the numerator and denominator by 2 we get a simplified fraction of 1/3. The value of the fraction is still the same, but the numbers are a little smaller, so we say the fraction has been simplified. 

For more help on simplifying fractions, check out the following website; 

http://www.mathsisfun.com/simplifying-fractions.html

As mentioned above, if you do have questions about any of this, feel free to comment on this post, or email or chat to me in person. 

A worksheet on this content can be found in the "Worksheets" tab above. I want all of the questions completed on this worksheet.