Transcript Chapter R, Section 2

Copyright © 2010 Pearson Education, Inc. All rights reserved.
R.1 – Slide 1
Prealgebra Review
Copyright © 2010 Pearson Education, Inc. All rights reserved.
R.1 – Slide 2
R.2
Decimals and Percents
Copyright © 2010 Pearson Education, Inc. All rights reserved.
R.1 – Slide 3
R.2 Decimals and Percents
Objectives
1.
2.
3.
4.
5.
6.
Write decimals as fractions.
Add and subtract decimals.
Multiply and divide decimals.
Write fractions as decimals.
Convert percents to decimals and decimals to percents.
Use fraction, decimal, and percent equivalents.
Copyright © 2010 Pearson Education, Inc. All rights reserved.
R.2 – Slide 4
R.2 Decimals and Fractions
Writing Decimals as Fractions
Converting a Decimal to a Fraction
Read the name using the correct place value.
Write it in fraction form just as you read it. The
denominator will be a power of 10, a number like
10, 100, 1000, and so on.
Copyright © 2010 Pearson Education, Inc. All rights reserved.
R.2 – Slide 5
R.2 Decimals and Fractions
Writing Decimals as Fractions
Example 1
Write each decimal as a fraction. Do not write in lowest terms.
(a) 0.85
85
This is read “85 hundredths.” So 0.85 
.
100
(b) 0.029
29
This is read “29 thousandths.” So 0.029 
.
1000
(c) 3.5907
This is read “3 and 5907 ten-thousandths”. So
3.5907  3 
5907
10, 000

30, 000
10, 000
Copyright © 2010 Pearson Education, Inc. All rights reserved.

5907
10, 000

35, 907
10, 000
R.2 – Slide 6
R.2 Decimals and Fractions
Adding and Subtracting Decimals
Example 2
Add or subtract as indicated.
(a) 13.129 + 0.25 + 5.6
1 3 .1 2 9
0 .2 5 0
Add decimals in a column. Make
sure the decimal points line up. + 5 .6 0 0
Attach zeros to
make all the
numbers the
same length.
18.979
(b) 2 – 0.329
Rewrite the operation in a
column.
2 .000
Attach zeros.
– 00.329
.329
1.671
Copyright © 2010 Pearson Education, Inc. All rights reserved.
R.2 – Slide 7
R.2 Decimals and Fractions
Multiplying and Dividing Decimals
Multiplying Decimals
Ignore the decimal points and multiply as if the
numbers were whole numbers. Then add together
the number of decimal places (digits to the right of
the decimal point) in each number being multiplied.
Place the decimal point in the answer that many
digits from the right.
Copyright © 2010 Pearson Education, Inc. All rights reserved.
R.2 – Slide 8
R.2 Decimals and Fractions
Multiplying and Dividing Decimals
Example 3
Multiply.
12.3 × 9.18
12.3
× 9.18
984
1 decimal place
2 decimal places
1+2=3
1230
110700
112.914
Copyright © 2010 Pearson Education, Inc. All rights reserved.
3 decimal places
R.2 – Slide 9
R.2 Decimals and Fractions
Multiplying and Dividing Decimals
Dividing Decimals
Change the divisor (the number you are dividing
by) into a whole number by moving the decimal
point as many places as necessary to the right.
Move the decimal point in the dividend (the
number you are dividing into) to the right by the
same number of places. Move the decimal point
straight up and then divide as with whole numbers.
Divisor
5
25 125
Quotient
Dividend
Copyright © 2010 Pearson Education, Inc. All rights reserved.
R.2 – Slide 10
R.2 Decimals and Fractions
Multiplying and Dividing Decimals
Example 4
Divide.
12.5  0.25
0.25 12.5 0
50 . 0
25 1250.
1250
0
So, 12.5  0.25 = 50
Copyright © 2010 Pearson Education, Inc. All rights reserved.
R.2 – Slide 11
R.2 Decimals and Fractions
Multiplying and Dividing Decimals
Multiplying or Dividing by Powers of 10
To multiply by a power of 10, move the decimal
point to the right as many places as the number
of zeros.
To divide by a power of 10, move the decimal
point to the left as many places as the number of
zeros.
In both cases, insert 0s as placeholders if
necessary.
Copyright © 2010 Pearson Education, Inc. All rights reserved.
R.2 – Slide 12
R.2 Decimals and Fractions
Multiplying and Dividing Decimals
Example 5
Multiply or divide as indicated.
a) 5.17624  1000  5176.24
We moved the decimal point three places to the right
because 1000 has three zeros.
b) 823.25  10,000  0.082325
We moved the decimal point four places to the left
because 10,000 has four zeros. We needed to insert
a zero in front of the 8 to do this.
Copyright © 2010 Pearson Education, Inc. All rights reserved.
R.2 – Slide 13
R.2 Decimals and Fractions
Multiplying and Dividing Decimals
Rule for Rounding
If the digit to become 0 or be dropped is 5 or more,
round up by adding 1 to the final digit to be kept.
If the digit to become 0 or be dropped is 4 or less,
do not round up.
Copyright © 2010 Pearson Education, Inc. All rights reserved.
R.2 – Slide 14
R.2 Decimals and Fractions
Writing Fractions as Decimals
Writing a Fraction as a Decimal
Because a fraction bar indicates division, write a
fraction as a decimal by dividing the denominator
into the numerator.
Copyright © 2010 Pearson Education, Inc. All rights reserved.
R.2 – Slide 15
R.2 Decimals and Fractions
Writing Fractions as Decimals
Example 6
Write
25
16
as a decimal.
1.5 6 2 5
16 25
16
90
80
10 0
96
40
32
80
80
0
Copyright © 2010 Pearson Education, Inc. All rights reserved.
25
16
= 1.5625
R.2 – Slide 16
R.2 Decimals and Fractions
Converting Percents to Decimals and Decimals to Percents
1% = 0.01
or
1% =
1
100
Example 7
Write 65% as a decimal.
65% = 65 · 1% = 65 · 0.01 = 0.65
Copyright © 2010 Pearson Education, Inc. All rights reserved.
R.2 – Slide 17
R.2 Decimals and Fractions
Converting Percents to Decimals and Decimals to Percents
Note
A quick way to change from a percent to a decimal is to
move the decimal point two places to the left and drop
the % symbol. To change from a decimal to a percent,
move the decimal point two places to the right and
attach a percent symbol.
Divide by 100;
Move 2 places left.
Decimal
Percent
Multiply by 100;
Move 2 places right.
Copyright © 2010 Pearson Education, Inc. All rights reserved.
R.2 – Slide 18
R.1 Fractions
Multiplying and Dividing Fractions
Example 8
Convert each percent to a decimal and each decimal to a percent.
a) 32% = 32. = 0.32
c) 0.95 = 0.95 = 95%
b) 175% = 175. = 1.75
d) 3.15 = 3.15 = 315%
Copyright © 2010 Pearson Education, Inc. All rights reserved.
R.2 – Slide 19