How to Subtract Decimals

decimals on a number lineMoney is usually the first time people use math in their lives. Every time you buy something, you can to calculate how much you need to give to the teller for the goods you just bought. If the buyer pays more than the price on the bill, the seller has to compute how much charge to give back. Both require subtracting decimals from another decimal number. To do this, we use the same strategy we use to subtract whole number. We only have to know where to put the decimal point in our answer. If you can do that, you will know how to subtract decimals. Learn how we use math every day at Udemy

Understanding Decimals

In order to subtract decimals, you need to know the role the decimal point plays in all of this. Decimals are fractions where the denominators are powers of 10. This includes such numbers as 7/10, 17/100, and 177/1000. We write these as decimals as 0.7, 0.17, and 0.177. The period is called a decimal point and it separates the decimal number from the whole number placed in from of it. We write a 0 for the whole number when there is none. The beauty of this format is that we can use it to write whole numbers as factions. We can write 23.46 as 2346/100, and 466 as 4600/100. We can also write whole numbers as decimals just by adding the point and as many zeroes to the right of the number. This is the main trick we use to subtract decimals from other numbers. Learn about decimals and fractions at Udemy

Subtracting Decimals

Subtracting decimals is as easy as subtraction whole numbers. The decimal point just adds extra digits. The trick is properly lining up the digits. Our number system writes values as sequences of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit in the number is assigned a power of 10. Whole numbers use positive powers of 10 to denote digit place while decimal numbers use negative powers. Negative powers are another way to write fractions where the numerator is 1. For instance, in the number 2356.974:

  • 2 is in the 103 position or 1000.
  • 3 is in the 102 position or 100.
  • 5 is in the 101 position or 10.
  • 6 is in the 100 position or 1.
  • 9 is in the 10-1 position, 1/10, or 0.1.
  • 7 is in the 10-2 position or 0.01.
  • 4 is in the 10-3 position or 0.001.

You subtract decimals from any number and any number from a decimal by lining up the digits according to their digit positions. If you need to you can add as many zeroes to the right of any number that needs them to make the two numbers line up properly. You then subtract the two numbers as if the decimal point didn’t exist. The purpose of the point is to tell you where the powers of 10 change sign, and nothing else. If you lined up the problem correctly, the decimal points in both your numbers should be above where the decimal point should go in your answer. Refresh your subtraction skills at Udemy

Subtracting Decimals from Whole Numbers

Now that you know the basic strategy, it is time for a few examples. We start with the simplest case of subtracting decimals from whole numbers. Let’s say you want to subtraction. 0.43 from 946. As you can see, 0.43 is a decimal number while 946 is a whole number without a decimal point. To subtract these numbers, you have to modify 946 so it has a decimal point. Generally, this means adding a decimal point after the whole number as well as many zeroes until it has the same number of decimal places as your decimal number. In our case, 043 has 2 decimal places. Therefore, you add two zeroes to 946 like this: 946 – 0.43 = 946.00 – 0.43. If you need to write the problem vertically, go ahead. The orientation doesn’t affect anything. You can write the above equations as: 946.00 -0.43 Do you see how each digit in one number aligns up with is corresponding digit in the other number? I added the zeroes after 946 so the two decimal points line up with each other. We then continue the subtraction as if the decimal points did not exist with one exception. Once we get to the points, we have to add a decimal point to our answer right then. If you lined up the problem correctly, you will notice that your decimal point lines up right underneath the other two decimal points. 946.00 -0.43 945.57

Subtracting Whole Numbers from Decimals

Nothing changes when you flip the problem over and subtract a whole number from a number with a decimal point. You just add a decimal point and the right amount of zeroes to the whole number and continue as normal. Just note that if your decimal number does not contain a whole number part, your answer should come out negative. Pure decimal numbers are fractions with a value that is less than 1. 0.43 -946.00 -945.57

Subtracting Decimals from Decimals

When both numbers contain decimals, you have a bit more work, but that much. You have to subtract numbers based on digit place which means each number needs to have the same number of digits to the right of their decimal points. If they don’t, you have to add zeroes to fill in the places until they do. You then subtract the two decimal numbers as you did before, ignoring the points until you come to them. That’s it. There is nothing more you need to know about subtracting decimals from decimals. 10346.8430 -8452.0305 1894.8125 Subtracting decimals from any number is as easy as understanding what decimals are and how the digits relate to each other. Decimal digits are defined so that they continue the same power of 10 factors we use with whole number digits. The trick is knowing that decimal points just mark where these powers of 10 change sign and become fractions. From there, you just have to do the math.