Transcript UNIT 3: DECIMAL FRACTIONS

Unit 3
Decimal Fractions
DECIMAL FRACTIONS
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1
UNITS
Written with a decimal point
Equivalent to common fractions having
denominators which are multiples of 10
The chart below gives the place value for
each digit in the number 1.234567
•
2
3
4
5
6
7
TENTHS
HUNDREDTHS
THOUSANDTHS
TEN
THOUSANDTHS
HUNDRED
THOUSANDTHS
MILLIONTHS
2
READING DECIMAL FRACTIONS
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To read a decimal, read number as whole
number.
Say name of place value of last digit to right.
•
0.567 is read “five hundred sixty-seven thousandths”
To read a mixed decimal (a whole number and
a decimal fraction), read whole number, read
word and at decimal point, and read decimal.
•
45.00753 is read “forty-five and seven hundred fiftythree hundred thousandths”
3
ROUNDING DECIMAL FRACTIONS
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Rounding rules:
• Determine place value to which number is to
•
be rounded
Look at digit immediately to its right
• If digit is less than 5, drop it and all digits to its right
• If digit is 5 or more, add 1 to digit in place to which
you are rounding. Then drop all digits to its right
4
ROUNDING EXAMPLES
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Round 14.763 to the nearest hundredth
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6 is in the hundredths place value, so look at 3. Since 3
is less than 5, leave 6 alone and drop 3.
Ans: 14.76
Round 0.0065789 to the nearest ten
thousandth
•
•
5 is in the ten thousandths place value, so look at 7.
Since 7 is greater than 5, raise 5 to 6 and drop all digits
to its right.
Ans: 0.0066
5
CONVERTING FRACTIONS TO
DECIMALS
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Fractions can be converted to decimals
by dividing the numerator by the
denominator
Express 5/8 as a decimal fraction:
.625 Ans • Place a decimal point after the 5 and
8 5.000
8
20
16
40
40
add zeros to the right of the decimal
point.
• Bring the decimal point straight up in
the answer. Divide.
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CONVERTING DECIMALS TO
FRACTIONS
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To change a decimal to a fraction, use
the number as the numerator and the
place value of the last digit as the
denominator
Change 0.015 to a common fraction:
• 0.015 is read as fifteen thousandths
15
3

Ans
1000 200
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ADDITION AND SUBTRACTION
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To add and subtract decimals, arrange
numbers so that decimal points are
directly under each other.
Add or subtract as with whole numbers
Place decimal point in answer directly
under the other decimal points
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ADDITION AND SUBTRACTION
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Perform the following operations:
13.475
+ 6.367
19.842 Ans
3.537
– 1.476
2.061 Ans
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MULTIPLICATION
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Multiply decimals using same procedures as
with whole numbers
Count total number of digits to right of decimal
points in both numbers being multiplied
Begin counting from last digit on right in
answer and place decimal point same number
of places as there are total in both of the
numbers being multiplied
10
MULTIPLICATION
Multiply 62.4  1.73:
• Since 62.4 has 1 digit to right of decimal and
1.73 has two points to right of decimal,
answer should have 3 digits to right of
decimal point
62.4
 1.73
1 872
43 68
62 4
107 952 = 107.952 Ans
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DIVISION
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Divide using the same procedure as with whole
numbers
Move the decimal point of the divisor as many
places as necessary to make it a whole
number
Move the decimal point in the dividend the
same number of places to the right
Divide and place the decimal point in the
answer directly above the decimal point in the
dividend
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DIVISION
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Divide 2.432 by 6.4:
• Move decimal point 1 place to right in 6.4
• Move decimal point 1 place to right in 2.432
• Place decimal point straight up in the answer
• Divide
.38 Ans
64 24.32
2
5 12
5 12
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POWERS
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Product of two or more equal factors
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Appear slightly smaller
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Located above and to right of number
being multiplied
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POWERS
Evaluate each of the following powers:
• .43
The power 3 means to multiply .4 by itself 3 times
.43 = .4 × .4 × .4 = .064 Ans
• (2.5 × 3)2
Parentheses first: 2.5 × .3 = .75
(.75)2 = .75 × .75 = .5625 Ans
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ROOTS
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A quantity that is taken two or more
times as an equal factor of a number
Finding a root is opposite operation of
finding a power
Radical symbol () is used to indicate
root of a number
• Index indicates number of times a root is to be
taken as an equal factor to produce the given
number
 Note: Index 2 for square root is usually omitted
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FINDING ROOTS
• Determine the following roots:
64
– This means to find the number that can be multiplied by
itself to equal 64. Since 8 × 8 = 64, the 64 = 8 Ans
3
27
– This means to find the number that can be multiplied
by itself three times to equal 27. Since 3 × 3 × 3 = 27,
3
27 = 3 Ans
Note: Roots that are not whole numbers can easily be computed using
a calculator
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ORDER OF OPERATIONS
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Order of operations including powers
and roots is:
• Parentheses
• Fraction bar and radical symbol are used as
grouping symbols
• For parentheses within parentheses, do innermost
parentheses first
• Powers and Roots
• Multiplication and division from left to right
• Addition and subtraction from left to right
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ORDER OF OPERATIONS
Solve (2.4  2)  36  2
2
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Parentheses and grouping symbols (square
root) first:
(1.2)2 + 6 ÷ 2
Powers next:
1.44 + 6  2
Divide:
1.44 + 3
Add:
4.44 Ans
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PRACTICE PROBLEMS
1.
Write the following numbers as words.
a. 0.0027
b. 143.45
c. 1.007368
2.
TENTHS
Round 10.2364579 to each of the
following place values:
HUNDREDTHS
THOUSANDTH
S
TEN
THOUSANDTH
S
HUNDRED
THOUSANDTHS
MILLIONTHS
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PRACTICE PROBLEMS (Cont)
3.
Express each of the following as decimal fractions:
1
a.
2
7
b.
8
15
c.
16
4. Express each of the following as fractions in lowest
terms:
a. 0.16
b. 0.1204
c. 0.635
5. Perform the indicated operations:
a. 0.0027 + 0.249 + 0.47
b. 6.45 + 2.576
c. 3.672 – 1.569
d. 45.3 – 16.97
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PRACTICE PROBLEMS (Cont)
e. 1.54 × 2.7
f. 25.63 × 3.46
g. 0.12  .4
h. 15.325  2.5
i. 0.33
j. (12.2 × .2)2
k. 3 64
l. 4.64  1.4  1.2 2  2
m. 3 8  2  (.6) 2  2
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Solutions
1.
Writing
a. Twenty-seven ten
thousandths
b. One hundred fortythree and forty-five
hundredths
c. One and seven
thousand three
hundred sixty-eight
millionths
2.
Rounding
1. 10.2
2. 10.24
3. 10.236
4. 10.2365
5. 10.23646
6. 10.236458
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Solutions
3. Convert to decimal
a. 0.5
b. 0.875
c. 0.9375
4. Decimal to Fraction
a. a4
25
301
2500
b. b
c. c127
200
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Solutions
5. Order of operations
a.
b.
c.
d.
e.
f.
g.
h.
i.
0.7217
9.026
2.103
28.33
4.158
88.6798
0.03
6.13
0.027
j.
k.
l.
m.
5.9536
4
5.32
3.82
25