Fundamentals of Mathematics, 2008a

496 CHAPTER 8. TECHNIQUES OF ESTIMATION
8.6 Summary of Key Concepts 6
8.6.1 Summary of Key Concepts
Estimation (Section 8.2)
Estimation is the process of determining an expected value of a computation.
Estimation By Rounding (Section 8.2)
The rounding technique estimates the result of a computation by rounding the numbers involved in the
computation to one or two nonzero digits. For example, 512 + 896 can be estimated by 500 + 900 = 1,400.
Cluster (Section 8.3)
When several numbers are close to one particular number, they are said to cluster near that particular
number.
Estimation By Clustering (Section 8.3)
The clustering technique of estimation can be used when
1. there are more than two numbers to be added, and
2. clustering occurs.
For example, 31 + 62 + 28 + 59 can be estimated by
(2 · 30) + (2 · 60) = 60 + 120 = 180
Distributive Property (Section 8.4)
The distributive property is a characteristic of numbers that involves both addition and multiplication.
For example,
3 (4 + 6) = 3 · 4 + 3 · 6 = 12 + 18 = 30
Estimation Using the Distributive Property (Section 8.4)
The distributive property can be used to obtain exact results for a multiplication.
For example,
15 · 23 = 15 · (20 + 3) = 15 · 20 + 15 · 3 = 300 + 45 = 345
Estimation by Rounding Fractions (Section 8.5)
Estimation by rounding fractions commonly rounds fractions to 1 4 , 1 2 , 3 4
, 0, and 1.
For example,
5
12 + 5 16 can be estimated by 1 2 + 1 4 = 3 4
8.7 Exercise Supplement 7
8.7.1 Exercise Supplement
8.7.1.1 Estimation by Rounding (Section 8.2)
For problems 1-70, estimate each value using the method of rounding. After you have made an estimate,
nd the exact value. Compare the exact and estimated values. Results may vary.
Exercise 8.7.1 (Solution on p. 509.)
286 + 312
Exercise 8.7.2
419 + 582
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