Concepts
1 BasicFunctions
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Unit 1C
Review of Operations with
Decimal Fractions and Percent
Copyright © Cengage Learning. All rights reserved.
1.11
Rounding Numbers
Copyright © Cengage Learning. All rights reserved.
Rounding Numbers
We often need to make an estimate of a number or a
measurement.
When a truck driver makes a delivery from one side of a
city to another, he or she can only estimate the time it will
take to make the trip.
An automobile technician must estimate the cost of a repair
job and the number of mechanics to assign to that job.
On such occasions, estimates are rounded.
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Rounding Numbers
Earlier, you found that
value to use in a calculation.
There is no exact decimal
You must round
to a certain number of decimal
places, depending on the accuracy needed in a given
situation.
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Example 1
Round 25,348 to the nearest thousand.
Note that 25,348 is more than 25,000 and less than 26,000.
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Rounding Numbers
Note:
If a number is exactly halfway between two numbers, round
up to the larger number.
Rounding Numbers to a Particular Place Value
To round a number to a particular place value:
1. If the digit in the next place to the right is less than 5,
drop that digit and all other following digits. Use zeros to
replace any whole-number places dropped.
2. If the digit in the next place to the right is 5 or greater,
add 1 to the digit in the place to which you are rounding.
Drop all other following digits. Use zeros to replace any
whole-number places dropped.
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Example 3
Round each number in the left column to the place
indicated in each of the other columns.
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Rounding Numbers
Instead of rounding a number to a particular place value,
we often need to round a number to a given number of
significant digits.
Significant digits are those digits in a number we are
reasonably sure of being able to rely on in a measurement.
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Rounding Numbers
Here we present a brief introduction to significant digits.
Significant Digits
The following digits in a number are significant:
• All nonzero digits (258 has three significant digits)
• All zeros between significant digits (2007 has four
significant digits)
• All zeros at the end of a decimal number (2.000 and
0.09500 have four significant digits)
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Rounding Numbers
The following digits in a number are not significant:
• All zeros at the beginning of a decimal number less than
1 (0.00775 has three significant digits)
• All zeros at the end of a whole number (36,000 has two
significant digits)
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Rounding Numbers
Rounding Numbers to a Given Number of Significant
Digits
To round a number to a given number of significant digits:
1. Count the given number of significant digits from left to
right, starting with the first nonzero digit.
2. If the next digit to the right is less than 5, drop that digit
and all other following digits. Use zeros to replace any
whole-number places dropped.
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Rounding Numbers
3. If the next digit to the right is 5 or greater, add 1 to the
digit in the place to which you are rounding. Drop all
other following digits. Use zeros to replace any
whole-number places dropped.
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Example 4
Round each number to three significant digits.
a. 74,123
Count three digits from left to right, which is the digit 1.
Since the next digit to its right is less than 5, replace the
next two digits with zeros. Thus, 74,123 rounded to three
significant digits is 74,100.
b. 0.002976401
Count three nonzero digits from left to right, which
is the digit 7. Since the next digit to its right is
greater than 5, increase the digit 7 by 1 and drop
the next four digits. Thus, 0.002976401 rounded to
three significant digits is 0.00298.
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