Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a...
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![Page 1: Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product. 0.7 0.03 = 7 10 3 100.](https://reader036.fdocuments.net/reader036/viewer/2022082516/56649cef5503460f949be207/html5/thumbnails/1.jpg)
Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product.
0.7 0.03 = 7
10
3
100
1 decimal place
2 decimal places
21
1000
= 0.021
=
3 decimal places
Multiplying Decimals
![Page 2: Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product. 0.7 0.03 = 7 10 3 100.](https://reader036.fdocuments.net/reader036/viewer/2022082516/56649cef5503460f949be207/html5/thumbnails/2.jpg)
Step 1: Multiply the decimals as though they were whole numbers.
Step 2: The decimal point in the product is placed so the number of decimal places in the product is equal to the sum of the number of decimal places in the factors.
Multiplying Decimals
![Page 3: Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product. 0.7 0.03 = 7 10 3 100.](https://reader036.fdocuments.net/reader036/viewer/2022082516/56649cef5503460f949be207/html5/thumbnails/3.jpg)
Examples1 Multiply: 6.78 × 0.05372 Multiply: 914.23 × 0.0132
![Page 4: Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product. 0.7 0.03 = 7 10 3 100.](https://reader036.fdocuments.net/reader036/viewer/2022082516/56649cef5503460f949be207/html5/thumbnails/4.jpg)
The only difference is the placement of a decimal point in the quotient. If the divisor is a whole number, divide as for whole numbers; then place the decimal point in the quotient directly above the decimal point in the dividend.
8
- 5 0 4
2 52
-2 52
0
divisor
quotient
dividend
0 4
Division of decimal numbers is similar to division of whole numbers.
63 52.92
Dividing by a Decimal
![Page 5: Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product. 0.7 0.03 = 7 10 3 100.](https://reader036.fdocuments.net/reader036/viewer/2022082516/56649cef5503460f949be207/html5/thumbnails/5.jpg)
8
63 52 9.2
- 504
25 2
-252
0
4
If the divisor is not a whole number, we need to move the decimal point to the right until the divisor is a whole number before we divide.
divisor dividend6 3 52 92. .
63 529 2. .
Dividing by a Decimal
![Page 6: Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product. 0.7 0.03 = 7 10 3 100.](https://reader036.fdocuments.net/reader036/viewer/2022082516/56649cef5503460f949be207/html5/thumbnails/6.jpg)
Dividing by a Decimal
Step 1: Move the decimal point in the divisor to the right until the divisor is a whole number.
Step 2: Move the decimal point in the dividend to the right the same number of places as the decimal point was moved in Step 1.
Step 3: Divide. Place the decimal point in the quotient directly over the moved decimal point in the dividend.
![Page 7: Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product. 0.7 0.03 = 7 10 3 100.](https://reader036.fdocuments.net/reader036/viewer/2022082516/56649cef5503460f949be207/html5/thumbnails/7.jpg)
Examples3 Divide: 0.084 ÷ 0.354 Divide and round to two decimal places:
0.004415 ÷ 0.032
![Page 8: Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product. 0.7 0.03 = 7 10 3 100.](https://reader036.fdocuments.net/reader036/viewer/2022082516/56649cef5503460f949be207/html5/thumbnails/8.jpg)
Estimating sums, differences, products, and quotients of decimal numbers is an important skill whether you use a calculator or perform decimal operations by hand.
Estimating Operations on Decimals
![Page 9: Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product. 0.7 0.03 = 7 10 3 100.](https://reader036.fdocuments.net/reader036/viewer/2022082516/56649cef5503460f949be207/html5/thumbnails/9.jpg)
Add 23.8 + 32.1.
Estimating When Adding Decimals
Exact Estimate
23.8+32.1
55.9
rounds to 24rounds to 32
56
This is a reasonable answer.
![Page 10: Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product. 0.7 0.03 = 7 10 3 100.](https://reader036.fdocuments.net/reader036/viewer/2022082516/56649cef5503460f949be207/html5/thumbnails/10.jpg)
When rounding to check a calculation, you may want to round the numbers to a place value of your choosing so that your estimates are easy to compute mentally.
Helpful Hint
![Page 11: Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product. 0.7 0.03 = 7 10 3 100.](https://reader036.fdocuments.net/reader036/viewer/2022082516/56649cef5503460f949be207/html5/thumbnails/11.jpg)
Multiply 32.3 1.9.
Estimating when Multiplying Decimals
Exact Estimate
32.3
1.9
290.7323.061.37
rounds to 32rounds to 2
64
This is a reasonable answer.
![Page 12: Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product. 0.7 0.03 = 7 10 3 100.](https://reader036.fdocuments.net/reader036/viewer/2022082516/56649cef5503460f949be207/html5/thumbnails/12.jpg)
Divide 258.3 ÷ 2.8
Estimating When Dividing Decimals
Exact Estimate
28. 2583. - 252 63 - 56 70 - 56 140 -140 0
rounds to 3 300100
This is a reasonable answer.
92.25
![Page 13: Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product. 0.7 0.03 = 7 10 3 100.](https://reader036.fdocuments.net/reader036/viewer/2022082516/56649cef5503460f949be207/html5/thumbnails/13.jpg)
Examples5 Estimate, then evaluate: 44.612 × 2.146 Divide. Round to two decimal places. 52
÷ 18