8.5: Summary of Key Concepts

Summary of Key Concepts

Estimation
Estimation is the process of determining an expected value of a computation.

Estimation By Rounding
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
When several numbers are close to one particular number, they are said to cluster near that particular number.

Estimation By Clustering
The clustering technique of estimation can be used when

there are more than two numbers to be added, and
clustering occurs.

For example, \(31 + 62 + 28 + 59\) can be estimated by
\((2 \cdot 30) + (2 \cdot 60) = 60 + 120 = 180\)

Distributive Property

The distributive property is a characteristic of numbers that involves both addition and multiplication. For example,
\(3(4 + 6) = 3 \cdot 4 + 3 \cdot 6 = 12 + 18 = 30\)

Estimation Using the Distributive Property
The distributive property can be used to obtain exact results for a multiplication.
For example,
\(15 \cdot 23 = 15 \cdot (20 + 3) = 15 \cdot 20 + 15 \cdot 3 = 300 + 45 = 345\)

Estimation by Rounding Fractions
Estimation by rounding fractions commonly rounds fractions to \(\dfrac{1}{4}, \dfrac{1}{2}, \dfrac{3}{4}\), 0 and 1.
For example,
\(\dfrac{5}{12} + \dfrac{5}{16}\) can be estimated by \(\dfrac{1}{2} + \dfrac{1}{4} = \dfrac{3}{4}\).