Download Section 1.1

Math in Our World
Section 1.2
Estimation and Interpreting
Graphs
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 Numbers
To 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
millionths
hundred-thousandths
ten-thousandths
thousandths
hundredths
tenths
ones
tens
hundreds
thousands
ten-thousands
hundred-thousands
millions
ten-millions
hundred-millions
billions
Rounding Numbers
If 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 2
Estimating 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 2
Estimating 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 3
Estimating 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 3
Estimating Remodeling Costs
SOLUTION
Step 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 Graph
A 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 Chart
Also 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.