Chapter 6: Decimals 75CHECK POINT
Complete each addition or subtraction.- 45.9 + 19.75
- 397.256 – 242.81
- 17,401.12 + 15,293.101
19. 159.41006 – 143.0025
20. 1.00027 + 0.4587332
Multiplying and Dividing Decimals
Multiplying decimals requires a slightly more complicated process. It’s a good idea to estimate
the product first, so if you have to multiply 3.1 v 2, you’d expect an answer around 3 v 2 or 6. If
you multiply 3.1 v 0.002, you’d recognize that you’re multiplying a number around 3 by a pretty
small number, quite a bit less than 1, so the answer should be less than 3, probably a lot less.
You perform the actual multiplication as though the decimal points were not present. If you were
multiplying 3.1 times 2, you would first think of it as 31 times 2. (You would also think of 3.1
times 0.002 as 31 times 2 to begin. The difference comes in placing the decimal point.)
To place the decimal point in the product, first count the number of digits to the right of the
decimal point in each of the factors being multiplied. Add these counts up to find the number of
decimal places in the product. Start from the far right end of the answer and count to the left to
place your decimal point.For example, multiply 3.1 v 2.
The first factor, 3.1, has one digit after the decimal point. The second factor, 2, has none, so the
product will have one digit after the decimal point.
Once you know that, multiply as if the decimal point wasn’t there. 31 v 2 = 62. Then place the
decimal point so that your answer has one digit after the decimal point. 3.1 v 2 = 6.2.
You estimated the answer as approximately 6, so 6.2 sounds quite reasonable. Let’s look at one
where the multiplier is smaller.Multiply 3.1 v 0.002.
This problem has the same important digits, so you’ll still start by thinking that 31 v 2 = 62, but
the decimal points are positioned differently.
Count the decimal places. There is one digit after the decimal point in 3.1. There are three digits
after the decimal point in 0.002, so the answer must have a total of 4 digits after the decimal point.