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 \(\dfrac{1}{2} + \dfrac{1}{4} = \dfrac{3}{4}\).