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Practice
1-3
Approximating Irrational Numbers
1-3
Approximating Irrational Numbers
1. On a number line, between which two consecutive whole numbers would
61 be located?
❍ A. 7 and 8
❍ C. 6 and 7
❍ B. 9 and 10
❍ D. 8 and 9
2. The height of a painting is
90 ft. Between which two consecutive whole
90 ?
numbers is
❍ A. 11 and 12
❍ C. 10 and 11
❍ B. 8 and 9
❍ D. 9 and 10
3. Estimate
15 to the nearest tenth. Then locate
15 on a number line.
4. Estimate
37 to the nearest hundredth. Then locate
37 on a number line.
5. The area of a square poster is 31 in.2. Find the length of one side of the poster
to the nearest tenth of an inch.
6. A tree is 16 feet tall. A wire runs from the top of the tree to a point 8 feet
from its base. The wire is 320 feet long. Estimate the length of the wire to
the nearest hundredth of a foot.
7. a) Writing On a number line, between which two consecutive whole numbers
would 381 be located?
❍ A. 19 and 20
❍ C. 18 and 19
❍ B. 20 and 21
❍ D. 21 and 22
b) Explain why it might be useful to approximate the value rather than use
the exact value.
8. Mental Math The volume of displacement in an engine is
which two consecutive whole numbers is 84 ?
❍ A. 8 and 9
❍ C. 10 and 11
❍ B. 11 and 12
❍ D. 9 and 10
9. Error Analysis Diego incorrectly said that
a) Estimate
84 L. Between
82 = 41.
82 to the nearest tenth.
b) What was his likely error?
❍ A. He evaluated 82 instead of evaluating
2
❍ B. He rounded incorrectly.
82 .
❍ C. He did not round.
❍ D. He evaluated the square root incorrectly.
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Practice 1-3
1
Homework G
10. a) Reasoning Estimate
35 to the nearest hundredth.
b) Is the estimated value rational or irrational? Explain.
11. The formula d = 2s 2 gives the length, d, of a diagonal of a square with side
length s. Each side of a square piece of wood is 33 cm long. You paint a stripe
along the diagonal of the piece of wood. Estimate the length of the stripe to
the nearest hundredth.
12. The length of a car is 162 ft. Will this car fit in a garage that measures
11 ft long? If not, what is the minimum length of a garage long enough for
this car?
13. Estimate
150 to the nearest hundredth.
14. Challenge A square pool has a volume of 4,528 cubic feet and a depth of
8 feet. A couple builds a fence 3.5 feet high around the pool. How many
square feet of fencing surround the pool? Round to the nearest tenth as
needed.
15. Challenge The formula D = TR gives the voltage D (in volts) across an
electrical circuit that uses power T (in watts) and has resistance R (in ohms).
Electrical Circuits
Circuit
Power (watts)
Resistance (ohms)
A
51
5
B
50
9
C
57
6
a) Estimate the voltage across each of these circuits to the nearest hundredth
of a volt.
b) List the circuits in order of the voltages from least to greatest.
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Practice 1-3
2
Homework G
ANSWER
KEY
Practice 1-3: Approximating Irrational Numbers
1. A
2. D
3. 3.9
4. 6.08
5. 5.6 in.
6. 17.89 ft
7. a) A
b) Answers will vary
8. D
9. a) 9.1
b) A
10. a) 5.92
b) The estimated value is rational because it terminates
and does not go on forever.
11. 46.67 cm
12. No, the car will not fit in the garage. The minimum length
of a garage long enough for the car is 13 ft.
13. 12.25
14. 333.2 ft2
15. a) Circuit A: 15.97 volts
Circuit B: 21.21 volts
Circuit C: 18.49 volts
b) A, C, B
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Practice 1-3
3
Answer Key G