Basic Mathematics for College Students

The rule for finding 10% of a number can be extended to help us quickly find
multiples of 10% of a number.

6.4 Estimation with Percent 553

Finding 10% of a Number

To find 10% of a number, move the decimal point in the number one place to

the left.

EXAMPLE (^2) What is 10% of 6,872 feet? Find the exact answer and an
estimate using front-end rounding.
StrategyTo find the exact answer, we will move the decimal point in 6,872 one
place to the left. To find an estimate, we will move the decimal point in an
approximation of 6,872 one place to the left.
WHYWe move the decimal point oneplace to the left because 10% of a number
means 0.10 of (times) the number.
Solution
Exact answer:
Move the understood decimal point
in 6,872 one place to the left.
Estimate:To estimate 10% of 6,872 feet, we can front-end round 6,872 to 7,000 and
find 10% of 7,000 feet. If we move the understood decimal point in 7,000 one place
to the left, we get 700. Thus,
10% of 6,872 feet700 feet Because 10% of 7,000 700.
10% of 6,872 feet687.2 feet
Self Check 2
What is 10% of 3,536 pounds?
Find the exact answer and an
estimate using front-end
rounding.
Now TryProblem 15

Caution! In Examples 1 and 2,front-end roundingwas used to find estimates
of answers to percent problems. Since there are other ways to approximate
(round) the numbers involved in a percent problem, the answers to estimation
problems may vary.
Finding 20%,30%,40%,...of a Number
To find 20% of a number, find 10% of the number by moving the decimal
point one place to the left, and then double (multiply by 2) the result. A
similar approach can be used to find 30% of a number, 40% of a number,
and so on.
EXAMPLE (^3) Estimate the answer: What is 20% of 416?
StrategyWe will estimate 10% of 416, and double (multiply by 2) the result.
WHY20% of a number is twice as much as 10% of a number.
SolutionSince 10% of 416 is 41.6 (or about 42 ), it follows that 20% of 416 is about
, which is 84.Thus,
20% of 416 84 Because 10% of 416 41.6 42 and 2  42 84.

2  42

Self Check 3

Estimate the answer: What is

20% of 129?

Now TryProblem 19