As mathematicians, we are obsessed with numbers! From the history of numbers to the ways in which we use them today, our modern world is overloaded with numbers, they just can’t be avoided. The time of day, the year, how fast we are allowed to drive, how hot it is outside… all of these are kept track of using numbers. 

We all know how to count to ten. But, did you know that there are multiple ways in which we can express the same number? For example, when we talk about two of something, we can use the word couple, the word pair, or the word duo. 

The same is true in mathematics. We can express the number two in different ways. 

How can that be the case? Well, welcome to the wonderful world of decimal fractions!

What Is A Decimal Fraction?

To understand decimal fractions, we must first make sure we understand both parts of the phrase.

As we know, a fraction is a number that represents a part of a whole. Some examples are a half (½), three-quarters (¾), or seven-eighths (⅞). Fractions have two parts, the top number, known as the numerator, and the bottom number, known as the denominator.

A decimal is a number, based on the number 10, that contains a decimal point. For example, the number 54.8 is a decimal.

Putting these definitions together, we can deduce that a decimal fraction is a fraction where the denominator is a number that is a power of ten, such as 10, 100, or 1000.

We can write the following decimal numbers as decimal fractions like so:

2.5 = 25/10
12.56 = 1256/100

We can also think of a decimal number as a whole number plus a decimal fraction:

2.5 = 2 and 5/10
12.56 = 12 and 56/100

Don’t forget, decimal numbers and decimal fractions can also be written as percentages:

38/100 = 38%

⅖ = 40%

Adding And Subtracting Decimals

Now that we’ve established what decimals are, we need to learn how they behave with one another, and how we can use them. The first step is to learn how to add and subtract decimals.

To add decimals, follow these steps:

• Write the numbers, one under the other, with the decimal points lined up;
• Put in zeros so the numbers have the same length;
• Then, using column addition, add them together;
• Remember to put the decimal point in the answer.

Similarly, to subtract decimals, take this approach:

• Write the numbers, one under the other, with the decimal points lined up;
• Add zeros so the numbers have the same length;
• Then subtract normally;
• Remember to put the decimal point in the answer.

Try it out for yourself on one of these handy worksheets.

Easy enough, right? Let’s take a quick look at something a bit more complex!

Multiplying And Dividing Decimals

Just as we can add and subtract decimals, so too can we multiply and divide them.

To multiply decimals, follow these steps:

• Multiply normally, ignoring the decimal points;
• Then put the decimal point in the answer → it will have as many decimal places as the two original numbers combined.

Put simply, count up how many numbers appear after the decimal point in each of the numbers you are multiplying. Your final answer should have the same number of numbers after the decimal, as the combined total of numbers you had after the decimal in the question.

To divide decimals, we have an even quicker shortcut:

• Multiply your number with a decimal (called the divisor, in this case) by 10 as many times as we need to until your original decimal number is written as a whole number;
• Multiply the dividend (the number you are dividing by) by the same number of tens. 

Still struggling to understand fully? Check out these helpful animations on dividing decimals. 

Converting Decimals To Fractions

The final step on our path toward understanding decimals is to learn how we convert decimals into fractions.

Once again, we have broken the process down into easy-to-follow steps:

• Write down the decimal divided by 1, like this:  0.75/1;
• Multiply both top and bottom by 10 for every number after the decimal point;
• Simplify the fraction.

If you need to convert a decimal to a fraction quickly, you can get used to the process by practicing on this conversion calculator.

A Full-Blown Curriculum In A Fraction Of The Time

At OMC, our online math courses are specially designed to help middle and high school math students excel in the subject, by plugging gaps in their knowledge, giving them a head start on their classmates, and getting them the all-important practice for testing environments.

Contact OMC today, to see how we can help kickstart your child’s math success.