Download Chapter 3

Chapter 3: Decimals
Section 3.1
Introduction to Decimals
3-2
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Examples
In each number, identify the place that the digit 7
occupies.
a. 68.75
b. 0.9657
c. 5.471
3-3
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Decimal Places and Positions
Each digit in a decimal place has a place value. The place
value system for decimals is an extension of the place value
system for whole numbers.
The numbers to the right of the decimal point are called
decimal places.
The following table shows the place values in the decimals
0.54 and 0.30716.
3-4
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Decimals and Fractions
To Change a Decimal to the Equivalent Fraction or Mixed
Number
• Copy the nonzero whole-number part of the decimal
and drop the decimal point.
• Place the fractional part of the decimal in the
numerator of the equivalent fraction.
• Make the denominator of the equivalent fraction 1
followed by as many zeros as the decimal has decimal
places.
• Simplify the resulting fraction, if possible.
3-5
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Example
Express each in fractional form and simplify.
a.
b.
c.
d.
e.
3-6
0.35
3.46
5.4
5.4000
4.29
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Examples
Write each number in decimal notation.
a. Nine tenths
b. Six and forty-seven ten-thousandths.
3-7
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Comparing Decimals
To Compare Decimals
• Rewrite the numbers vertically, lining up the decimal
points.
• Working from left to right, compare the digits that have
the same place value. The decimal which has the largest
digit with this place value is the largest decimal.
3-8
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Examples
1. Which is larger: 0.813 or 0.84?
2. Rank from smallest to largest: 1.13, 1.1, and 0.31.
3-9
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Rounding
3-10
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Rounding Decimals
To Round a Decimal to a Given Decimal Place
• Underline the digit in the place to which the number
is to be rounded.
• Look at the digit to the right of the underlined digit
– the critical digit. If the digit is 5 or more, add 1 to
the underlined digit; if it is less than 5, leave the
underlined digit unchanged.
• Drop all decimal places to the right of the
underlined digit.
3-11
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Example
Round 46.271 to
3-12
a.
the nearest tenth
b.
two decimal places
c.
nearest thousandth
d.
the nearest ten
e.
the nearest whole number
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Example
1. Round 6.961 to the nearest tenth.
2. The price of a gallon of gas is often expressed in
terms of thousandths. Suppose that the price of a
gallon of gas is $3.269. What is the price to the
nearest cent?
3-13
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Section 3.2
Adding and Subtracting Decimals
3-14
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Adding and Subtracting Decimals
To Add Decimals
1. Rewrite the numbers vertically, lining up the decimal
points.
2. Replace missing decimal places with 0’s.
3. If adding, add the digits.
4. If subtracting, subtract borrowing when necessary.
5. Insert a decimal point in the sum or difference below
the other decimal points.
3-15
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Examples
1. Find the sum: 4.9 + 72.38 + 8.059
2. Compute: 9.14 + 6 + 7.46
3. By noon, the rain gauge recorded 0.08 inches of
rain. In the next 24 hours, another 1.25 inches
were recorded. What was the total rainfall?
3-16
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Examples
1. Subtract and check: 8.072 – 5.63
2. 32 is how much larger than 4.07?
3. Madison competes in a marathon (26.2 miles).
After running 17.8 miles, how much further does
she have to run?
3-17
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Estimating
Being able to estimate in your head the sum
or difference between two decimals is a useful
skill, if only for checking an exact answer. To
estimate, simply round the numbers to be
added or subtracted and then carry out the
operation on the rounded number.
3-18
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Examples
1.
2.
3.
4.
5.
3-19
Compute: 0.48 + 0.7 + 0.089
Subtract 0.923 – 0.064, then check by estimating.
Combine and check: 0.72 – (0.21 + 0.0758)
Julian’s cat weights 11.7 lbs and his dog weighs
39.4 lbs. Estimate to find how much more his dog
weighs than his cat.
Compute: 4.7 + 3.1 + 7.5 using your calculator.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.