8 Chapter 1 Whole Numbers
WHY To round to the nearest hundred, the digit in the hundreds column is the
rounding digit and the digit in the tens column is the test digit.
Solution
a.First, we find the rounding digit in the hundreds column, which is 3. Then we
look at the test digit 4 to the right of 3 in the tens column. Because 4 5, we
round down and leave the 3 in the hundreds column. We then replace the two
rightmost digits with 0’s.
Rounding digit: hundreds column Keep the rounding digit: Do not add 1.
18,349 18,349
Test digit: 4 is less than 5. Replace with 0’s.
Thus, 18,349 rounded to the nearest hundred is 18,300.
b.First, we find the rounding digit in the hundreds column, which is 9. Then we look
at the test digit 6 to the right of 9. Because 6 is 5 or greater, we round up and
increase 9 in the hundreds column by 1. Since the 9 in the hundreds column
represents 900, increasing 9 by 1 represents increasing 900 to 1,000. Thus, we
replace the 9 with a 0 and add 1 to the 7 in the thousands column. Finally, we
replace the two rightmost digits with 0’s.
Add 1. Since 9 + 1 = 10, write 0 in this
Rounding digit: hundreds column column and carry 1 to the next column.
7,960
Test digit: 6 is 5 or greater. Replace with 0s.Thus, 7,960 rounded to the nearest hundred is 8,000.^7
7 1
, 90
60
EXAMPLE (^8) U.S. Cities In 2007,
Denver was the nation’s 26th largest city.
Round the 2007 population of Denver shown
on the sign to:
a.the nearest thousand
b.the nearest hundred thousand
Strategy In each case, we will find the
rounding digit and the test digit.
WHY We need to know the value of the test digit to determine whether we round
the population up or down.
Solution
a.The rounding digit in the thousands column is 8. Since the test digit 3 is less than
5, we round down. To the nearest thousand, Denver’s population in 2007 was
588,000.
b.The rounding digit in the hundred thousands column is 5. Since the test digit 8 is
5 or greater, we round up. To the nearest hundred thousand, Denver’s
population in 2007 was 600,000.
Denver
CITY LIMIT
Pop. 588, 349 Elev. 5,280
Self Check 8
U.S. CITIESRound the elevation
of Denver:
a.to the nearest hundred feet
b.to the nearest thousand feet
Now TryProblems 75 and 79
6 Read tables and graphs involving whole numbers.
The following table is an example of the use of whole numbers. It shows the number
of women members of the U.S. House of Representatives for the years 1997–2007.
Caution! To round a number, use onlythe test digit directly to the right of the
rounding digit to determine whether to round up or round down.