Subtracting Decimals Is Easy: Find Out How To Do It
Decimal subtraction shows up in a lot of areas, including money management. Need to learn how to manage your money? There are a lot of good online classes that will show you how.
Decimals – What’s the Point?
First, let’s have a quick rundown on decimal numbers. The bottom line is that they’re just regular numbers, only with a fraction tacked on at the end (the right-hand side). The fraction is shown in a special form — in tenths, hundredths, thousandths, etc.
What do we mean? Here’s a regular number: 117. That’s just one hundred and seventeen, of course. So, how do we write one hundred and seventeen and one tenth? We could do it like this: 117 1/10. But we could also write it as a decimal number: 117.1. What about one hundred and seventeen and one hundredth? It’s 117 1/100, and it’s also 117.01. And one hundred seventeen and one thousandth? That’s 117 1/1,000 as well as 117.001.
Ten Times Smaller With Each Step
Each step to the right of the decimal point that you go, the numbers are just divided by ten one more time: one tenth (0.1), one hundredth (0.01), one thousandth (0.001), one ten-thousandth (0.0001), etc. It’s like regular, non-decimal numbers, where each step to the left is ten times greater (tens, hundreds, thousands, etc.), only you divide instead of multiply. When you go to the right or the left in a decimal number, you’re just walking down the magical path.
Any Kind of Fraction
We said that in a decimal number, everything to the right of the decimal place is a fraction, and as it turns out, any number that can be shown as a regular fraction (and a bunch that can’t) can also be shown as a decimal fraction. We won’t go into the details, because they can get kind of complicated, but here are a couple of basic examples:
You know what 1/4 is — it’s just one quarter. If you divide a chocolate bar into four equal pieces, each one is 1/4 the size of the original chocolate bar. What happens if you divide the number 100 into four equal pieces? Each piece is equal to 25, which is 1/4 of 100. To turn 1/4 into a decimal fraction, you just divide 1 by 4, which gives you 0.25, or twenty-five hundredths.
Try another one: 1/8. You can divide 8 into 1,000 and get 125 — so if you divide 8 into 1, you get 0.125, or one hundred and twenty-five thousandths.
(Notice the zero to the left of the decimal point? It’s not necessary, but it’s a useful way of reminding yourself that there’s a decimal point there, since the decimal itself is small, and easy to miss. Sometimes zeroes are good for keeping track of things. Keep that in mind, because zeroes are going to turn up again in just a moment.)
Take it Away!
OK. Let’s look at subtraction. When it comes to standard, non-decimal numbers, you know the basics: line the numbers up on the right (at the ones’ place) with the one you want to subtract below the one that you want to subtract from, start from the right, working your way left, and if the number on top is smaller than the one on the bottom, borrow from the next digit to the left. Like this:
172 - 39 ---- 133
Since 2 is smaller than 9, you borrowed 1 from the 7 to the right to turn 2 into 12. Subtracting 9 from 12 gives you 3. When you borrowed (stole, really, because you aren’t going to give it back) the 1 from 7, the 7 turned into a 6, so you subtract 3 from 6 in the tens’ place, to give you 3. And the lower number doesn’t have anything in the hundreds’ place, so you just drop the 1 down, giving you 133.
Where Does It Go?
Time to subtract some decimal numbers. First’ we’ll pick a number: 23.2756. What number should we subtract from it? Let’s try 1.164.
But they aren’t the same length, so we need to figure out how to line them up. If we line them up on the right, the way we do with non-decimal numbers, we’ll have decimal points in two locations, and we’ll be subtracting tenths from hundredths, and hundredths from thousandths. That doesn’t look right at all. So what can we do?
Line ‘Em Up!
How about lining the decimal points up? that puts the ones under the ones, the tenths under the tenths, and everything else just where it should be:
23.2756 - 1.164 -------- 22.1116
Do you see how that worked? It was exactly like the example we gave before, with whole numbers. The only difference was that we lined up the decimals first.
Take a Number
Now look at this example:
11.5418 - 2.16 -------- 9.3818
See what happened? To subtract the 6 from the 4, we borrowed 1 from the 5, turning the 4 into 14, just the way you would with non-decimal numbers. (And notice that that’s what we did with the 11 and the 2 to the left of the decimal point.)
Taking Something From Nothing?
That really is easy, isn’t it? Here’s one last (and very simple) trick. Remember how we said that zeroes are good for keeping track of things? Take a look at these numbers: 4.73 and 2.1261. How do you subtract the one on the right from the one on the left? if you just line up the decimal points, the 61 part isn’t going to be sitting under anything at all:
4.73 -2.1261 ------- ??????
What do you subtract it from? The air?
Zero is the Hero!
If you put zeroes in those empty spaces, everything should start to become clear:
4.7300 -2.1261 ------- 2.6039
4.73 and 4.7300 are really the same number, but once you put the zeroes there, it’s much easier to see how to subtract: you borrow (that is, steal) from the numbers to the left to turn the zeroes into something larger, and then you can subtract.
There’s much more to learn about numbers, of course, and good reason to learn more: you need them in everything from personal finance and business to woodworking, gourmet cooking, and electronic engineering. Why not check out a few of the many online classes and see what’s available?
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