Amy has a master's degree in secondary education and has been teaching math for over 9 years. Amy has worked with students at all levels from those with special needs to those that are gifted.
We see decimals every day. They are your numbers with a decimal point and some numbers behind that decimal point. Think of the numbers you see when you go shopping, and you are thinking of decimal numbers. You see your favorite shoes on sale for $45.99, and you are looking at a decimal.
Any number with a decimal point is a decimal number. The famous math number, pi, is a decimal that begins with 3.14159. When you start experimenting with different numbers on your calculator, you will see that decimal numbers happen very often. If you divide 5 by 8, you get 5/8, which equals 0.625. 8 divided by 13 is 0.6153846...
Did you notice that the answer to 8 divided by 13 is a decimal number that continues forever, like the number pi? It's impossible to completely write out the whole decimal. So, in math, this is where rounding our decimals comes in. Rounding decimals isn't about writing our decimals all nice and round, but it is about shortening our decimals so that we only write a few digits while trying to keep the number as accurate as possible.
You lose accuracy when you round a decimal, but you get a number that is easier to use. For example, is 3.14159265359 easier to use or 3.14? Of course, the shorter one is easier to use. Yes, 3.14 is the rounded decimal number of 3.14159265359, which is just the beginning of the number pi.
How to Round
To round decimals, we first decide how short we want our rounded decimal. For this, we need to know our number places. For example, are we rounding to the tenths (one place), hundredths (two places), or thousandths (three decimal places)? The tenths place tells us that we want to shorten our decimal so that it only has one number after the decimal point. The hundredths place is two numbers after the decimal point. The thousandths place is the third number after the decimal point.
Once we have decided how short we want our decimal, we now look at the numbers that are being cut off, the numbers to the right of our last desired digit, specifically the digit that is directly to the right of our last desired digit. If this digit is less than 5, specifically if it is 0, 1, 2, 3, or 4, then we keep our last desired digit the same and we are done rounding. But if this digit is 5 or greater than 5, specifically, if it is 5, 6, 7, 8, or 9, then we make our last desired digit go up by one.
To help you with this, think of the two groups of numbers as two baseball teams. Which group of numbers is higher? It is the group of 5, 6, 7, 8, and 9. We call this group 'Team Up.' The other group, then, is 'Team Down.' If you see a number in Team Up, then you know you need to up your last desired digit by 1. If you see a number in Team Down, you keep your last desired digit the same.
Let's look at some examples now.
Rounding 5.6386 to three decimal places gives us 5.639. The last digit we want to keep is the 8. The digit directly to the right of our last desired digit is a 6. 6 is in Team Up, so we increase our last desired digit, our 8, by 1 to get 9.
Rounding 2.54089 to two decimal places gives us 2.54 because the digit directly to the right of our last desired digit is 0. 0 is in Team Down, so we keep our last desired digit, the 4, the same.
Rounding 6.89 to the ones place gives us 7, because the digit to the right of the ones place is 8. 8 is in Team Up, so we add 1 to our last desired digit, which is the 6.
We've now finished covering how to round decimals. Let's review what we've learned. We've learned that decimals are the numbers with a decimal point and some numbers behind that decimal point.
To round them, we first decide how short we want our rounded number. We decide what decimal place we are rounding to. We then take a look at the number directly to the right of our desired place. If it is 0, 1, 2, 3, or 4, we keep our last digit the same, and we are done rounding. If it is 5, 6, 7, 8, or 9, we increase our last digit by 1.
Once you are done with this lesson you should be able to round a decimal number to the desired decimal place.
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