OPERATIONS WITH DECIMALS
2•3
2•3
Operations with
Decimals
Adding and Subtracting Decimals
Adding and subtracting decimals is similar to adding and
subtracting whole numbers.
EXAMPLE Adding and Subtracting Decimals
Add 6.75 + 29.49 + 16.9.
6.75
29.49
+ 16.9
_______
1
6.75
29.49
+ 16.9
_______
4
2
6.75
29.49
+
16.9
_______
14
• Line up the decimal points.
• Add or subtract the place farthest
right. Rename, if necessary.
• Add or subtract the next place left.
Rename, if necessary.
• Continue with the whole numbers.
6.75
29.49
Place the decimal point in the result.
+ 16.9
_______
53.14
So, 6.75 + 29.49 + 16.9 = 53.14.
Check It Out
Solve.
1 1.387 + 2.3444 + 3.45
3 56.13 - 17.59
110 HotTopics
2 0.7 + 87.8 + 8.174
4 826.7 - 24.6444
Multiplying Decimals
Multiplying decimals is much the same as multiplying whole
numbers.
EXAMPLE Multiplying Decimals
Multiply 42.8 · 0.06.
42.8
428
× 0.06
× 6
______
______
2568
2568
42.8
× 0.06
______
2.568
• Multiply as with whole
numbers.
• Add the number of decimal
1 decimal place
2 decimal places
places for the factors, and
place
the decimal point in the
1 + 2 = 3 decimal places
product.
So, 42.8 · 0.06 = 2.568.
Check It Out
Multiply.
5 22.03 · 2.7
6 9.655 · 8.33
7 11.467 · 5.49
Estimating Decimal Products
To estimate decimal products, you can replace given numbers
with compatible numbers. Compatible numbers are estimates
you choose because they are easier to work with mentally.
Estimate 26.2 · 52.3.
• Replace the factors with compatible numbers.
30
52.3
50
26.2
• Multiply mentally.
30 · 50 = 1,500
Operations with Decimals
111
2•3
Check It Out
Estimate each product by using compatible numbers.
8 12.75 · 91.3
9 3.76 · 0.61
10 25.25 · 1.95
OPERATIONS WITH DECIMALS
Dividing Decimals
Dividing decimals is similar to dividing whole numbers.
EXAMPLE Dividing Decimals
Divide 38.35 ÷ 6.5.
6.5 · 10 = 65
• Multiply the divisor by a power of ten to make it
a whole number.
• Multiply the dividend by the same power of ten.
38.35 · 10 = 383.5
5.9
65. 383.5
• Divide. Place the decimal point in the quotient.
325
_______
58 5
- 58 5
______
0
So, 38.35 ÷ 6.5 = 5.9.
Check It Out
Divide.
11 211.68 ÷ 9.8
12 42.363 ÷ 8.1
13 444.36 ÷ 4.83
14 1.548 ÷ 0.06
112 HotTopics
Zeros in Division
You can use zeros as placeholders in the dividend when you are
dividing decimals.
EXAMPLE Zeros in Division
Divide 375.1 ÷ 6.2.
6.2 · 10 = 62
375.1 · 10 = 3,751
60.
62. 3751.
- 372
______
31
-0
____
31
60.5
62. 3751.0
372
______
31
0
____
310
310
_____
0
So, 375.1 ÷ 6.2 = 60.5.
• Multiply the divisor and the dividend by
a power of ten. Place the decimal point.
• Divide. Place the decimal point.
• Use zeros as placeholders in the dividend.
Continue to divide.
Check It Out
Divide until the remainder is zero.
15 0.7042 ÷ 0.07
16 37.2 ÷ 1.5
17 246.1 ÷ 0.8
Operations with Decimals
113
Rounding Decimal Quotients
You can use a calculator to divide decimals and round quotients.
OPERATIONS WITH DECIMALS
2•3
EXAMPLE Rounding Decimals on a Calculator
Divide 6.3 by 2.6. Round to the nearest hundredth.
• Use your calculator to divide.
6.3
2.6
2.4230769
• Look at the digit one place to the right
2.4230769
of the hundredths place.
•
2.4230769 rounds to 2.42.
Round.
Some calculators have a “fix” function. Press
and the
number of decimal places you want. The calculator will then
display all numbers rounded to that number of places. Consider
2.6
in a calculator.
the example above. Again, enter 6.3
.
Since you want to round to the nearest hundredth press
The answer
2.42 is shown in the display.
Check It Out
Solve with a calculator. Round to the nearest hundredth.
18 0.0258 ÷ 0.345
19 0.817 ÷ 1.25
20 0.4369 ÷ 0.267
21 0.3112 ÷ 0.4
114 HotTopics
2•3
Exercises
Add.
1. 256.3 + 0.624
2. 78.239 + 38.6
3. 7.02396 + 4.88
4. $250.50 + $385.16
5. 2.9432 + 1.9 + 3 + 1.975
Subtract.
6. 43 - 28.638
7. 58.543 - 0.768
8. 435.2 - 78.376
9. 38.3 - 16.254
10. 11.01 - 2.0063
Multiply.
11. 0.66 · 17.3
13. 7.526 · 0.33
15. 22.4 · 9.4
12. 0.29 · 6.25
14. 37.82 · 9.6
Divide until the remainder is zero.
16. 29.38 ÷ 0.65
17. 62.55 ÷ 4.5
18. 84.6 ÷ 4.7
19. 0.657 ÷ 0.6
Divide. Round to the nearest hundredth.
20. 142.7 ÷ 7
21. 2.55 ÷ 1.6
22. 22.9 ÷ 6.2
23. 15.25 ÷ 2.3
24. The Moon orbits Earth in 27.3 days. How many orbits does
the Moon make in 365.25 days? Round your answer to the
nearest hundredth.
25. Apollo 15 astronauts drove the lunar rover about
27.8 kilometers on the Moon. Their average speed was
3.3 kilometers/hour. How long did they drive the lunar
rover?
Operations with Decimals
115