4-7 Convert Between Systems
Complete. Round to the nearest hundredth if necessary.
1. 5 in. ≈ ____________ cm
SOLUTION: Since 1 inch ≈ 2.54 centimeters, multiply by .
So, 5 inches is approximately 12.7 centimeters.
ANSWER: 12.7
2. 2 qt ≈ __________ mL
SOLUTION: Since 946.35 milliliters ≈ 1 quart, multiply by .
So, 2 quarts is approximately 1,892.7 milliliters. ANSWER: 1,892.7 mL
3. 58.14 kg ≈ ___________ lb
SOLUTION: Since 1 pound ≈ 0.4536 kilogram, multiply by .
So, 58.14 kilograms is approximately 128.17 pounds.
ANSWER: 128.17
4. 4 L ≈ __________ gal
SOLUTION: Since 1 gallon ≈ 3.79 liters, multiply by .
eSolutions Manual - Powered by Cognero
So, 4 liters is approximately 1.06 gallons. Page 1
So, 58.14 kilograms is approximately 128.17 pounds.
ANSWER: 4-7 Convert
Between Systems
128.17
4. 4 L ≈ __________ gal
SOLUTION: Since 1 gallon ≈ 3.79 liters, multiply by .
So, 4 liters is approximately 1.06 gallons. ANSWER: 1.06 gallons
5. 10 mL ≈ ___________ c
SOLUTION: Since 1 cup ≈ 236.59 milliliters, multiply by .
So, 10 milliliters is approximately 0.04 cup.
ANSWER: 0.04
6. 63.5 T ≈ __________ kg
SOLUTION: Since 1 ton ≈ 907.2 kilograms, multiply by .
So, 63.5 tons is approximately 57,607.2 kilograms.
ANSWER: 57,607.2
7. 4.725 m ≈ ___________ ft
SOLUTION: Since 1 foot ≈ 0.30 meter, multiply by eSolutions Manual - Powered by Cognero
.
Page 2
So, 63.5 tons is approximately 57,607.2 kilograms.
ANSWER: 4-7 Convert
Between Systems
57,607.2
7. 4.725 m ≈ ___________ ft
SOLUTION: Since 1 foot ≈ 0.30 meter, multiply by .
So, 4.725 meters is approximately 15.75 feet.
ANSWER: 15.75
8. 3 T ≈ __________ kg
SOLUTION: Since 1 ton ≈ 907.2 kilograms, multiply by .
So, 3 tons is approximately 2,721.6 kilograms.
ANSWER: 2,721.6
9. 680.4 g ≈ __________ lb
SOLUTION: Since 1 pound ≈ 453.6 grams, multiply by .
So, 680.4 grams is approximately 1.5 pounds.
ANSWER: 1.5
10. A notebook computer has a mass of 2.25 kilograms. About how many pounds does the notebook weigh?
SOLUTION: Since 1 pound ≈ 0.4536 kilogram, multiply by eSolutions Manual - Powered by Cognero
.
Page 3
So, 680.4 grams is approximately 1.5 pounds.
ANSWER: 4-7 Convert
Between Systems
1.5
10. A notebook computer has a mass of 2.25 kilograms. About how many pounds does the notebook weigh?
SOLUTION: Since 1 pound ≈ 0.4536 kilogram, multiply by .
The notebook weighs approximately 4.96 pounds.
ANSWER: 4.96 lb
11. A glass bottle holds 3.75 cups of water. About how many milliliters of water can the bottle hold?
SOLUTION: Since 1 cup is about equal to 236.59 milliliters, multiply by
.
So, 3.75 cups is approximately 887.21 mL.
ANSWER: 887.21 mL
12. A Cabbage Palmetto has a height of 80 feet. What is the approximate height of the tree in meters?
SOLUTION: Since 1 foot ≈ 0.30 meter, multiply by .
The tree is approximately 24 meters tall.
ANSWER: 24 m
Persevere with Problems Determine the greater amount for the situation.
13. Which box is greater, a 1.5-pound box of raisins or a 650-gram box of raisins?
SOLUTION: Since 1 pound ≈ 453.6 grams, multiply 1.5 pounds by eSolutions Manual - Powered by Cognero
.
Page 4
The tree is approximately 24 meters tall.
ANSWER: 4-7 Convert
Between Systems
24 m
Persevere with Problems Determine the greater amount for the situation.
13. Which box is greater, a 1.5-pound box of raisins or a 650-gram box of raisins?
SOLUTION: Since 1 pound ≈ 453.6 grams, multiply 1.5 pounds by .
So, 1.5 pounds is approximately 680.4 grams. Since 680.4 g > 650 g, a 1.5-pound box of raisins is greater than a 650gram box.
ANSWER: 1.5 lb
14. Which is greater a 2.75-gallon container of juice or a 12-liter container of juice?
SOLUTION: Since 3.79 liters is approximately 1 gallon, multiply by
.
Since 10.4225 < 12, the 12-liter container of juice is greater.
ANSWER: 12 liter
15. Reason Inductively One gram of water has a volume of 1 milliliter. What is the volume of the water if it has a
mass of 1 kilogram?
SOLUTION: Since 1 gram of water has a volume of 1 milliliter and 1 kilogram = 1,000 grams, then 1 kilogram, or 1,000 grams, of
water has a volume of 1,000 × 1 milliliter or 1,000 milliliters, which is also equivalent to 1 L.
ANSWER: 1,000 mL or 1 L
16. Persevere with Problems The distance from Earth to the Sun is approximately 93 million miles. About how many
gigameters is this? Round to the nearest hundredth. (Hint: In 1 gigameter there are about 621,118.01 miles.)
SOLUTION: Since 1 gigameter ≈ 621,118.01 miles, multiply by eSolutions Manual - Powered by Cognero
.
Page 5
Since 1 gram of water has a volume of 1 milliliter and 1 kilogram = 1,000 grams, then 1 kilogram, or 1,000 grams, of
water has a volume of 1,000 × 1 milliliter or 1,000 milliliters, which is also equivalent to 1 L.
ANSWER: 4-7 Convert
Between Systems
1,000 mL or 1 L
16. Persevere with Problems The distance from Earth to the Sun is approximately 93 million miles. About how many
gigameters is this? Round to the nearest hundredth. (Hint: In 1 gigameter there are about 621,118.01 miles.)
SOLUTION: Since 1 gigameter ≈ 621,118.01 miles, multiply by .
So, the distance from the Earth to the Sun is approximately 149.73 gigameters.
ANSWER: about 149.73 gigameters
Be Precise Order the set of measures from greatest to least.
17. 1.2 cm, 0.6 in., 0.031 m, 0.1 ft
SOLUTION: Convert each measure to meters.
Convert 1.2 centimeters to meters.
Use the relationship 1 centimeter = 0.01 meter.
Convert 0.6 inch to meters.
Since 1 inch ≈ 2.54 centimeters and 1 centimeter = 0.01 meter, multiply by or .
Convert 0.1 foot to meters.
Since 1 foot ≈ 0.3 meter, multiply by .
eSolutions
Manual
- Powered by
Cognerometer,
So, 1.2
centimeters
is 0.012
Since
0.6 inch is approximately 0.02 meter, and 0.1 foot is approximately 0.03 meter.Page 6
, the order from greatest to least is 0.031 m, 0.1 ft, 0.6 in. and 1.2 cm.
So, the distance from the Earth to the Sun is approximately 149.73 gigameters.
ANSWER: 4-7 Convert
Between Systems
about 149.73 gigameters
Be Precise Order the set of measures from greatest to least.
17. 1.2 cm, 0.6 in., 0.031 m, 0.1 ft
SOLUTION: Convert each measure to meters.
Convert 1.2 centimeters to meters.
Use the relationship 1 centimeter = 0.01 meter.
Convert 0.6 inch to meters.
Since 1 inch ≈ 2.54 centimeters and 1 centimeter = 0.01 meter, multiply by or .
Convert 0.1 foot to meters.
Since 1 foot ≈ 0.3 meter, multiply by .
So, 1.2 centimeters is 0.012 meter, 0.6 inch is approximately 0.02 meter, and 0.1 foot is approximately 0.03 meter.
Since
, the order from greatest to least is 0.031 m, 0.1 ft, 0.6 in. and 1.2 cm.
ANSWER: 0.031 m, 0.1 ft, 0.6 in., 1.2 cm
18. 2 lb, 891 g, 1 kg, 0.02 T
SOLUTION: Convert each measure to grams.
Convert 2 pounds to grams.
Since 1 pound is 453.6 grams, multiply by
eSolutions
Manual
- Powered by
Convert
1 kilogram
toCognero
grams.
1 kilogram = 1,000 grams
.
Page 7
Since
, the order from greatest to least is 0.031 m, 0.1 ft, 0.6 in. and 1.2 cm.
ANSWER: 4-7 Convert
Between
Systems
0.031 m, 0.1
ft, 0.6 in.,
1.2 cm
18. 2 lb, 891 g, 1 kg, 0.02 T
SOLUTION: Convert each measure to grams.
Convert 2 pounds to grams.
Since 1 pound is 453.6 grams, multiply by
.
Convert 1 kilogram to grams.
1 kilogram = 1,000 grams
Convert 1 ton to grams.
Since 1 ton ≈ 907.2 kilograms and 1 kilogram = 1,000 grams, multiply by or .
So, 2 pounds is approximately 907.2 grams, 1 kilogram is 1,000 grams, and 0.02 ton is approximately 18,144 grams.
Since
, the order from greatest to least is 0.02 T, 1 kg, 2 lb, 891 g.
ANSWER: 0.02 T, 1 kg, 2 lb, 891 g
19. c, 0.4 L, 950 mL, 0.7 gal
SOLUTION: Convert each measure to milliliters.
Convert
cups to milliliters.
Since 1 cup = 236.59 milliliters, multiply by
.
Convert 0.4 liter to milliliters.
Use the relationship 1 liter = 1,000 milliliters.
eSolutions Manual - Powered by Cognero
Convert 0.7 gallon to milliliters.
Page 8
So, 2 pounds is approximately 907.2 grams, 1 kilogram is 1,000 grams, and 0.02 ton is approximately 18,144 grams.
Since
, the order from greatest to least is 0.02 T, 1 kg, 2 lb, 891 g.
ANSWER: 4-7 Convert
Between Systems
0.02 T, 1 kg, 2 lb, 891 g
19. c, 0.4 L, 950 mL, 0.7 gal
SOLUTION: Convert each measure to milliliters.
Convert
cups to milliliters.
Since 1 cup = 236.59 milliliters, multiply by
.
Convert 0.4 liter to milliliters.
Use the relationship 1 liter = 1,000 milliliters.
Convert 0.7 gallon to milliliters.
Since 1 gallon ≈ 3.79 liters and 1 liter = 1,000 milliliters, multiply by So,
or .
cup is approximately 295.74 milliliters, 0.4 liter is 400 milliliters, and 0.7 gallon is approximately 2,653 milliliters. Since
mL, 0.4 L,
, the order from greatest to least is 0.7 gal, 950
c.
ANSWER: 0.7 gal, 950 mL, 0.4 L,
c
20. 4.5 ft, 48 in., 1.3 m, 120 cm
SOLUTION: Convert each measure to centimeters.
Convert 4.5 feet to centimeters.
Since 1 foot is 30 centimeters, multiply by
eSolutions Manual - Powered by Cognero
.
Page 9
ANSWER: 4-7 Convert
Between
0.7 gal, 950
mL, 0.4 Systems
L,
c
20. 4.5 ft, 48 in., 1.3 m, 120 cm
SOLUTION: Convert each measure to centimeters.
Convert 4.5 feet to centimeters.
Since 1 foot is 30 centimeters, multiply by
.
Convert 48 inches to centimeters.
Since 1 inch ≈ 2.54 centimeters, multiply by .
Convert 1.3 meters to centimeters.
1.3 meters = 130 centimeters
So, 4.5 feet is approximately 135 centimeters, 48 inches is approximately 121.92 centimeters, and 1.3 meters is 130
centimeters. Since
, the order from greatest to least is 4.5 ft, 1.3 m,
48 in., 120 cm.
ANSWER: 4.5 ft, 1.3 m, 48 in., 120 cm
inches to centimeters. Round to the nearest tenth. Then
21. Model with Mathematics Convert inches and
draw a segment whose length is between those two measures. SOLUTION: Change each fraction into a decimal, and then convert each measurement to centimeters.
So,
.
So,
1 inch is approximately 2.54 centimeters, so multiply by
eSolutions Manual - Powered by Cognero
.
Page 10
centimeters. Since
48 in., 120 cm.
, the order from greatest to least is 4.5 ft, 1.3 m,
ANSWER: 4-7 Convert
Between Systems
4.5 ft, 1.3 m, 48 in., 120 cm
inches to centimeters. Round to the nearest tenth. Then
21. Model with Mathematics Convert inches and
draw a segment whose length is between those two measures. SOLUTION: Change each fraction into a decimal, and then convert each measurement to centimeters.
So,
.
So,
1 inch is approximately 2.54 centimeters, so multiply by
.
. So,
and
See students' work for drawings.
ANSWER: 5.4 cm; 6.7 cm; See students' work for drawings
Complete. Round to the nearest hundredth if necessary.
22. 15 cm ≈ ___________ in.
SOLUTION: Since 1 inch ≈ 2.54 centimeters, multiply by .
So, 15 centimeters is approximately 5.91 inches.
ANSWER: 5.91
23. 350 lb ≈ _________ kg
SOLUTION: eSolutions Manual - Powered by Cognero
Since 1 pound ≈ 0.4536 kilogram, multiply by Page 11
.
So, 15 centimeters is approximately 5.91 inches.
ANSWER: 4-7 Convert
Between Systems
5.91
23. 350 lb ≈ _________ kg
SOLUTION: Since 1 pound ≈ 0.4536 kilogram, multiply by .
So, 350 pounds is approximately 158.76 kilograms.
ANSWER: 158.76
24. 17 mi ≈ __________ km
SOLUTION: Since 1 mile ≈ 1.61 kilometers, multiply by .
So, 17 miles is approximately 27.37 kilometers.
ANSWER: 27.37
25. 32 gal ≈ __________ L
SOLUTION: Since 1 gallon ≈ 3.79 liters, multiply by .
So, 32 gallons is approximately 121.28 liters.
ANSWER: 121.28
26. 50 mL ≈ ___________ fl oz
SOLUTION: Since 1 cup ≈ 236.59 milliliters and 1 cup = 8 fluid ounces, multiply by eSolutions Manual - Powered by Cognero
.
Page 12
So, 32 gallons is approximately 121.28 liters.
ANSWER: 4-7 Convert
Between Systems
121.28
26. 50 mL ≈ ___________ fl oz
SOLUTION: Since 1 cup ≈ 236.59 milliliters and 1 cup = 8 fluid ounces, multiply by .
So, 50 milliliters is approximately 1.69 fluid ounces.
ANSWER: 1.69
27. 19 kg ≈ ___________ lb
SOLUTION: Since 1 pound ≈ 0.4536 kilogram, multiply by .
So, 19 kilograms is approximately 41.89 pounds.
ANSWER: 41.89
28. The Willis Tower has a height of 1,451 feet. What is the estimated height of the building in meters?
SOLUTION: Since 1 foot ≈ 0.30 meter, multiply by .
The Willis Tower is approximately 435.3 meters tall.
ANSWER: 435.3 m
29. Which is greater, a bottle containing 64 fluid ounces of water or a bottle containing 2 liters of water?
SOLUTION: Since 1 cup ≈ 236.59 milliliters, 1 liter = 1,000 milliliters, and 1 cup = 8 fluid ounces, multiply 64 fluid ounces by eSolutions Manual - Powered by Cognero
or .
Page 13
The Willis Tower is approximately 435.3 meters tall.
ANSWER: 4-7 Convert
Between Systems
435.3 m
29. Which is greater, a bottle containing 64 fluid ounces of water or a bottle containing 2 liters of water?
SOLUTION: Since 1 cup ≈ 236.59 milliliters, 1 liter = 1,000 milliliters, and 1 cup = 8 fluid ounces, multiply 64 fluid ounces by or .
So, 64 fluid ounces is approximately 1.89 liters. Since 1.89 L < 2 L, the bottle containing 2 liters of water is greater.
ANSWER: 2L
30. Use Math Tools A bakery uses 900 grams of peaches in a cobbler. About how many pounds of peaches does the
bakery use in a cobbler?
SOLUTION: Since 1 pound ≈ 453.6 grams, multiply by .
The bakery uses about 1.98 pounds of peaches.
ANSWER: 1.98 lb
Determine which quantity is greater.
31. 3 gal, 10 L
SOLUTION: Since 1 gallon ≈ 3.79 liters, multiply 3 gallons by .
So, 3 gallons is approximately 11.37 liters. Since 11.37 L > 10 L, 3 gallons is greater.
ANSWER: 3 gal
eSolutions Manual - Powered by Cognero
32. 14 oz, 0.4 kg
SOLUTION: Page 14
The bakery uses about 1.98 pounds of peaches.
ANSWER: 4-7 Convert
Between Systems
1.98 lb
Determine which quantity is greater.
31. 3 gal, 10 L
SOLUTION: Since 1 gallon ≈ 3.79 liters, multiply 3 gallons by .
So, 3 gallons is approximately 11.37 liters. Since 11.37 L > 10 L, 3 gallons is greater.
ANSWER: 3 gal
32. 14 oz, 0.4 kg
SOLUTION: Since 1 pound = 16 ounces and 1 pound ≈ 0.4536 kilogram, multiply 14 ounces by .
So, 14 ounces is approximately 0.3969 kilogram. Since 0.3969 kg < 0.4 kg, 0.4 kilograms is greater.
ANSWER: 0.4 kg
33. 4 mi, 6.2 km
SOLUTION: Since 1 mile ≈ 1.61 kilometers, multiply 4 miles by .
So, 4 miles is approximately 6.44 kilometers. Since 6.44 km > 6.2 km, 4 miles is greater.
ANSWER: 4 mi
34. Velocity is a rate usually expressed in feet per second or meters per second. How can the units help you calculate
velocity using the distance a car traveled and the time recorded?
SOLUTION: eSolutions
Manual - Powered by Cognero
Page 15
The units feet/second and meters/second each show a distance divided by a time. Therefore you would calculate
velocity by dividing the distance a car traveled by the time recorded.
So, 4 miles is approximately 6.44 kilometers. Since 6.44 km > 6.2 km, 4 miles is greater.
ANSWER: 4-7 Convert
Between Systems
4 mi
34. Velocity is a rate usually expressed in feet per second or meters per second. How can the units help you calculate
velocity using the distance a car traveled and the time recorded?
SOLUTION: The units feet/second and meters/second each show a distance divided by a time. Therefore you would calculate
velocity by dividing the distance a car traveled by the time recorded.
Sample answer: The rate meters/second indicates division, so velocity is distance divided by time.
ANSWER: Sample answer: The rate meters/second indicates division, so velocity is distance divided by time.
35. The diagram shows the length of a fork from the cafeteria.
Which measurements are approximately equal to the length of the fork? Select all that apply
15.2 cm 0.152 m 152 cm 1.52 m
SOLUTION: Convert the inches into centimeters, and then convert centimeters into meters.
Since 1 inch ≈ 2.54 centimeters, multiply by .
The fork is approximately 15.2 centimeters. The first measurement is correct, while 152 cm is not.
Convert centimeters into meters. Since 1 meter = 100 centimeters, multiply by .
The fork is approximately 0.152 meters. The second measurement is correct, while the fourth is not.
ANSWER: 15.2 cm 0.152 m 152 cm 1.52 m
36. The masses of 4 different animals from a zoo are shown in the table. Convert each measure to pounds. Then sort the animals from least to greatest weight.
eSolutions Manual - Powered by Cognero
Page 16
4-7 Convert Between Systems
Convert each measure to pounds. Then sort the animals from least to greatest weight.
How many pounds greater is the heaviest animal than the lightest animal?
Explain how you can use units to be sure you are multiplying by the correct fraction when converting between
measurement systems. Give an example.
SOLUTION: Convert kilograms to pounds. Since 1 pound ≈ 0.4536 kilograms, multiply by Brown Bear:
.
So, the brown bear weighs approximately 600 pounds.
Giraffe:
So, the giraffe weighs approximately 2,500 pounds.
Lion:
So, the lion weighs approximately 500 pounds.
Rhinoceros:
So, the lion weighs approximately 3500 pounds.
Comparing all of the weights, the animals from least to greatest weight would be: lion, brown bear, giraffe, and
eSolutions Manual - Powered by Cognero
Page 17
rhinoceros.
To determine how many pounds greater the heaviest animal is than the lightest animal, subtract 500 pounds from
4-7 Convert Between Systems
So, the lion weighs approximately 3500 pounds.
Comparing all of the weights, the animals from least to greatest weight would be: lion, brown bear, giraffe, and
rhinoceros.
To determine how many pounds greater the heaviest animal is than the lightest animal, subtract 500 pounds from
3,500 pounds.
3,500 lb - 500 lb = 3,000 lb.
So, the difference between the two weights is 3,000 pounds.
Sample answer: When converting between measurement systems, you need to make sure that you can divide out
common units. For example, to convert 226.8 kilograms to pounds, multiply 226.8 kg by
common units are divided out, you are left with
or 500 pounds.
. When the
ANSWER: ; 3,000 lb; Sample answer: When converting between
measurement systems, you need to make sure that you can divide out common units. For example, to convert
226.8 kilograms to pounds, multiply 226.8 kg by
left with
or 500 pounds.
. When the common units are divided out, you are
Convert. Round to the nearest tenth if necessary.
37. 17 ft = __________ yd
SOLUTION: Since 1 yard = 3 feet, multiply by
.
ANSWER: 5.7
38. 82 in. = _________ ft
SOLUTION: Since 1 foot = 12 inches, multiply by
eSolutions Manual - Powered by Cognero
.
Page 18
ANSWER: 4-7 Convert
Between Systems
5.7
38. 82 in. = _________ ft
SOLUTION: Since 1 foot = 12 inches, multiply by
.
ANSWER: 6.8
39. 3 mi = _________ ft
SOLUTION: Since 5,280 feet = 1 mile, multiply by
.
ANSWER: 15,840
40. A skyscraper is 0.484 kilometer tall. What is the height of the skyscraper in meters?
SOLUTION: Use the relationship 1 kilometer = 1,000 meters.
The height of the skyscraper is 484 meters.
ANSWER: 484 m
eSolutions Manual - Powered by Cognero
Page 19