552 Chapter 6 Percent
SECTION 6.4
Estimation with Percent
Objectives
1 Estimate answers to percent
problems involving 1% and
10%.
2 Estimate answers to percent
problems involving 50%, 25%,
5%, and 15%.
3 Estimate answers to percent
problems involving 200%.4 Use estimation to solve percent
application problems.Estimationcan be used to find approximations when exact answers aren’t necessary.
For example, when dining at a restaurant, it’s helpful to be able to estimate the amount
of the tip. When shopping, the ability to estimate a discount or the sale price of an item
also comes in handy. In this section, we will discuss some estimation methods that can
be used to make quick calculations involving percents.1 Estimate answers to percent problems involving 1% and 10%.
There is an easy way to find 1% of a number that does not require any calculations.
First, recall that. Thus, to find 1% of a number, we multiply it by 0.01,
and a quick way to multiply the number by 0.01 is to move its decimal point two places
to the left.1% 1001 0.01
Finding 1% of a NumberTo find 1% of a number, move the decimal point in the number two places to
the left.EXAMPLE (^1) What is 1% of 423.1? Find the exact answer and an estimate
using front-end rounding.
StrategyTo find the exact answer, we will move the decimal point in 423.1 two
places to the left. To find an estimate, we will move the decimal point in an
approximation of 423.1 two places to the left.
WHYWe move the decimal point twoplaces to the left because 1% of a number
means 0.01 of (times) the number.
Solution
Exact answer:
Move the decimal point in 423.1 two places to the left.
Estimate:Recall from Chapter 1 that with front-end rounding,a number is
rounded to its largest place value so that all but its first digit is zero. To estimate 1%
of 423.1, we can front-end round 423.1 to 400 and find 1% of 400. If we move the
understood decimal point in 400 two places to the left, we get 4. Thus,
1% of 423.1 4 Because 1% of 400 4.
1% of 423.14.23 1
Self Check 1
What is 1% of 519.3? Find the
exact answer and an estimate
using front-end rounding.
Now TryProblem 11
Success Tip To quickly find 2% of a number, find 1% of the number by
moving the decimal point two places to the left, and then double (multiply by
2) the result. In Example 1, we found that 1% of 423.1 is 4.231. Thus, 2% of
423.1 is. A similar approach can be used to find 3% of a
number, 4% of a number, and so on.
2 4.2318.462
There is also an easy way to find 10% of a number that doesn’t require any
calculations. First, recall that. Thus, to find 10% of a number, we
multiply the number by 0.1, and a quick way to multiply the number by 0.1 is to move
its decimal point one place to the left.