Chapter 3 - Decimals. After reading this chapter, you should have a good understanding of the following learning objectives: Explain the place values of whole numbers and decimals; round decimals; convert decimal fractions to decimals, proper fractions to decimals, mixed numbers to decimals, and pure and mixed decimals to decimal fractions; add, subtract, multiply, and divide decimals; complete decimal applications in foreign currency; multiply and divide decimals by shortcut methods.
Trang 1Decimals
Trang 21 Explain the place values of whole
numbers and decimals; round decimals
proper fractions to decimals, mixed numbers to decimals, and pure and mixed decimals to decimal fractions
Decimals
#3
Learning Unit Objectives
Rounding Decimals; Fraction and Decimal Conversions
LU3.1
32
Trang 31 Add, subtract, multiply, and divide
decimals
methods
currency
Decimals
#3
Learning Unit Objectives
Adding, Subtracting, Multiplying, and Dividing Decimals
LU3.2
Trang 4Decimal Percent
55
55
55
55
55
55
55 = 1
Trang 5Figure 3.1
100
1 1,000 1 .
10,000
1
100,000
and Whole Number Groups Decimal Place Values
Trang 6Rounding Decimals
Step 1. Identify the place
value of the digit you want
to round
Step 2. Identify the digit to the right
If 5 or more, increase the identified digit
by 1. If less than 5 do not change
Step 3. Drop all digits to the right
of the identified digit
.33
Trang 7Round to nearest dollar: $166.39 $166
Round to nearest cent: $1,196.885 $1,196.89 Round to nearest hundredth: $38.563 $38.56
Round to nearest thousandth: $1,432.9981 $1,432.998
Trang 8Converting Decimal Fractions to Decimals
2 Steps
1. Count the number of zeros
in the denominator
2. Place the numerator of the
decimal fraction to the
right of the decimal point
the same number of
places as you have zeros
in the denominator. Do
not go over the total
number of denominator
zeros
Fraction Decimal # of places
10
100
1,000
10,000
Trang 93 4
4 3.00 2.8 20 20 0
EQUA
LS
.75
Step 1
Trang 10Converting Mixed Numbers to Decimals
2 5
5 2.0 2.0 0
8.4
.4
(St ep
1)
Trang 1124 1 24
24 100
2
.24
Step 1
Step 2
Step 3 Places
Trang 12Converting Mixed Decimals to
Decimal Fractions
45 1 45
45 45
100 100
2
17.45
Step 1
Step 2
Step 3 Places
=17
Trang 13Add: 4 + 7.3 + 36.139 + .0007 + 8.22
4.0000 7.3000 36.1390 .0007 8.2200
Trang 14Subtracting Decimals
Subtract: 45.3 15.273
45.300
15.273
30.027
Trang 152.36
x .016
57084 3 decimal places 57.084
3776 5 decimal places 03776
8.52 (2 decimal places)
x 6.7 (1 decimal places)
Need to add zero
Trang 16Dividing Decimals
Step 1. Make the divisor a
whole number by moving
the decimal point to the right
Step 2. Move the decimal point
in the dividend to the right
the same number of places
as in step 1. If there are not
enough places, add zeros to the right
of the dividend.
Step 3. Place the decimal point
in the quotient above the
new decimal point in the
dividend. Divide as usual
2.5 32.800
25. 328.00
25. 328.00
25
78
75
30
25
50
50
13.12
Example
Trang 17Check $29.11 x 6.8348 = 198.96 yuan
Each 1 equal 6.8348 yuan
The Wall Street Journal clip shows in China the price of Microsoft
Office was reduced to 199 yuan from an original price of 699
yuan. Using the currencies table lets us see what the original as
well as sales price is in U.S. dollars. In the table on page 74 1 yuan equals $.1463. To find the original selling price you multiply the
number of yuan (699) times $.1463.
699 yuan x $.1463 = $102.26
The original selling price in U.S. Dollars is $102.26. To find the
new selling price in U.S. dollars, you multiply the number of yuan
199 times $.1463. The new selling price in U.S. dollars is $29.11.
$199 x $.1463 = $29.11 Table factor from currency table on page 74
Trang 186.89 x 10
6.89 x 100
6890
689
•Count the zeros in the multiplier
•Move the decimal point the same number of spaces to the right
Multiplication
Trang 19Shortcuts for Multiples of 10
6.89 / 10
6.89 / 100
.00689
•Count the zeros in the divisor
•Move the decimal point the same number of spaces to the left
Division