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Multiplying Signed Decimal Numbers
Steps for Multiplying Decimals
1.
Ignore decimals and multiply as before
2.
Count the number of digits after the
decimal in the original problem and make
sure the answer has the same number of
digits after the decimal.
Simplify the following:
1.
0.07(0.03)
2.
–0.42(6)
7(3)
- 42 ( 6 )
21
- 252
4 decimal places
0.0021
2 decimal places
-2.52
3.
3.12(0.05)
4.
–0.02(–1.39)
312 ( 5 )
- 2 ( -139 )
1560
278
4 decimal places
0.1560
4 decimal places
0.0278
5.
1.22
1.2 ( 1.2 )
12 ( 12 )
6.
(- 0.3)2
- 0.3 ( - 0.3 )
-3(-3)
144
9
1.44
0.09
7.
0.5(22)
8.
10(.314)
5 ( 22 )
10 ( 314 )
110
3140
11.0
3.14
9. 100(.314)
100 ( 314 )
31400
31.4
10. 1000(.314)
1000 ( 314 )
314000
314
11. What is the perimeter of a rectangular
field that measures 4.2 miles by 3.1
miles? P = 2l + 2w
P = 2(4.2) + 2(3.1)
P = 2(42) + 2(31)
P = 84 + 62
8.4
+ 6.2
P = 8.4 + 6.2
The perimeter of the rectangular
field is 14.6 miles.
12. What is the area of a rectangular field
that measures 4.2 miles by 3.1 miles?
A = bh
A = (4.2)(3.1)
A = (42)(31)
A = 1302
A = 13.02
The area of the rectangular
field is 13.02 square miles.
13. John worked 63.5 hours over the past
two weeks. John earns $9.50 per hour.
How much money did John earn?
John’s earnings = (63.5)(9.50)
John’s earnings = (635)(95)
John’s earnings = 60325
John’s earnings = 603.25
John earned $603.25.
14. Jill filled up the gas tank in her new
hybrid car. Jill put 10.39 gallons of gas
in her car at a rate of $2.39 per gallon.
How much did she pay for gas?
Gas Bill = (10.39)(2.39)
Gas Bill = (1039)(239)
Gas Bill = 248321
Gas Bill = 24.83
Jill purchased $24.83 worth of gas.
15. What is the volume of a rectangular
cube with dimensions 3.2 feet by
4.1 feet by 1.1 feet?
Volume = (3.2)(4.1)(1.1)
V = (32)(41)(11)
V = 14432
V = 14.432
The volume of the rectangular
cube is 14.432ft3.
Dividing Signed Decimal Numbers
Steps for dividing by whole numbers
1. Use long division as if there were no decimal
point involved.
2. If necessary, add zeros after last digit in the
decimal.
3. Place decimal point directly above the
decimal point in the problem.
Divide the following:
4 65
1. 8 37.2 0
32
52
48
40
40
0
7 87
2.  4  31.48
-28
-34
-32
-28
-28
0
Steps for dividing by decimals numbers
1.
Change divisor to a whole number by
moving both numbers the same amount
of digits
2.
Divide as before
6 66
3. 33
3.3 219
21.978
.78
198
217
198
19 8
198
0
Divide the following:
Divide the following:
33
4. 22
0.22 726
7.26
66
66
66
0
5.
.3778 ÷ .25 and round to the nearest
hundredth:
1 5 11 1.51
0
0.25
.3778
25
370.78
25
127
125
When rounding make
28
sure to calculate one
25
digit past required
30
place value.
25
6.
4.579 + 34.8 ÷ (–4)
4.579 + 34.8 ÷ (–4)
4.579 + ( -8.7 )
- 8.700
+ 4.579
-4.121
-8 7
 4 34.8
32
28
28
0
7.
(3.07 – 0.43) ÷ 0.33
(3.07 – 0.43) ÷ 0.33
2.64 ÷ 0.33
8
3.07
– 0.43
2.64
8
033
.33 264
2.64
264
0
8.
6 – (0.3)2 ÷ 10
6 – (0.3)2 ÷ 10
6 – 0.09 ÷ 10
6 – 0.09 ÷ 10
6 – 0.009
6.000
– 0.009
5.991
0.3 (0.3)
3 (3)
9
0.09
009
10 0.090
90
0
9. Jill filled up the gas tank in her new hybrid
car. Jill put 10.3 gallons of gas in her car and she
had driven 473.8 miles. Estimate the gas
mileage then determine how many miles per
gallon her car achieved?
470 miles ÷ 10 gallons
47 mpg
9. Jill filled up the gas tank in her new hybrid
car. Jill put 10.3 gallons of gas in her car and she
had driven 473.8 miles. Estimate the gas
mileage then determine how many miles per
gallon her car achieved?
47 mpg
46
4738
10103
.3 473
.8
412
618
618
0
Jill can get 46
miles per gallon
while driving
her hybrid car.