Section 1.2Estimation and Interpreting

Graphs

Math in Our World

Learning Objectives

Round numbers to a given level of accuracy. Estimate the answers to real-world problems. Use estimation to obtain information from

graphs.

Rounding NumbersTo round numbers, use these rules:

1. Locate the place-value digit of the number that is being rounded. Here is the place-value chart for whole numbers and decimals:

8, 9 8 5, 7 3 0, 2 6 1 . 2 3 5 6 7 5

billio

ns

hun

dre

d-millio

ns

ten-m

illion

s

millio

ns

hun

dre

d-thou

sand

s

ten-th

ousan

ds

thou

san

ds

hun

dre

ds

tens

one

s

tenth

s

hun

dre

dths

thou

san

dth

s

ten-th

ousan

dth

s

hun

dre

d-tho

usa

nd

ths

millio

nths

Rounding NumbersIf the digit to the right of the place-value digit is 0 through 4, then do not change the place-value digit.

If the digit to the right of the place-value digit is 5 through 9, add 1 to the place-value digit.

Note: When you round decimal numbers, drop all digits to the right of the digit that is being rounded.

EXAMPLE 1 Rounding Numbers

Round each number to the place value given.

(a) 7.328 (ones)

(b) 15.683 (hundredths)

(c) 32.4817 (tenths)

(d) 0.047812 (ten-thousandths)

Estimation

When you estimate answers for numerical calculations, two steps are required.

1. Round the numbers being used to numbers that make the calculation simple.

2. Perform the operation or operations involved.

EXAMPLE 2Estimating the Cost of a Cell Phone

You’re considering a new cell phone plan where you have to pay $179 up front for the latest phone, but the monthly charge of $39.99 includes unlimited minutes and messaging.

Estimate the cost of the phone for 1 year if there are no additional charges.

EXAMPLE 2Estimating the Cost of a Cell Phone

SOLUTION

Step 1 We can round the cost of the phone to $180 and the monthly charge to $40.

Step 2 The monthly cost estimate for 1 yr is

$40 x 12 = $480. (12 months in a year)

Add the estimated cost of the phone$480 + $180 = $660. (monthly charge + up front charge)

Our estimated cost for 1 year is $660.

EXAMPLE 3Estimating Remodeling Costs

The Fabeets family plans on remodeling their living room. They will be replacing 21 square yards of carpet at a cost of $23 per yard and having 16 linear feet of wall papered at a cost of $32 per foot.

Estimate the total cost of the remodel.

EXAMPLE 3Estimating Remodeling Costs

SOLUTIONStep 1 We can round the size and cost of the carpet

to 20 square yards and $25 per square yard. We can also round the length and cost of the wall to 15 feet and $30 per foot.

Step 2 The estimated carpet cost is

20 x $25 = $500. (area of carpet times cost)

The estimated wallpaper cost is

15 x $30 = $450. (length of wall times cost)

Our estimated cost for 1 year is $500 + $450 = $950.

Bar GraphA graph used to compare amounts or percents using either vertical or horizontal bars of various lengths which correspond to the amounts or percents.

EXAMPLE 4 Obtaining Information from a Bar Graph

The graph shown represents the percent of electricity generated by nuclear energy in five countries.

Find the approximate percent of electricity generated by nuclear energy in France.

EXAMPLE 4 Obtaining Information from a Bar Graph

SOLUTION

The first vertical bar represents the percentage for France.

Reading across from the height of the bar to the vertical axis, we see that the height is a little bit more than halfway between 70 and 80%, so we estimate that the answer is about 76%.

Pie ChartAlso called a circle graph, is constructed by drawing a circle and dividing it into parts called sectors, according to the size of the percentage of each portion in relation to the whole.

EXAMPLE 5 Obtaining Information from a Pie Chart

The pie chart shown represents the number of fatal occupational injuries in the United States for a selected year. If the total number of fatal injuries was 5,915 for the year, estimate how many resulted from assaults and violent acts.