Lesson 5.1 Rational Numbers Worksheet Page 3
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To write a terminating decimal as a
Writing Decimals as Fractions
fraction or a mixed number, use the place of the last digit to determine
the denominator of the fraction, as shown in Example 4. Example 5
Note Worthy
shows a method for writing a repeating decimal as a fraction.
In your notebook, you may
want to include a list of
Example 4
Writing Terminating Decimals as Fractions
common fraction-decimal
equivalents. You can refer to
7
the list when solving problems,
a.
0.7
7 is in tenths’ place, so denominator is 10.
1
0
or you may want to memorize
the list. Here are some
5
5 is in hundredths’ place, so denominator
3.05
3
b.
examples you might include:
1
00
is 100.
1
1
0.5,
0.3 ,
1
2
3
3
Simplify fraction.
2
0
1
1
0.25,
0.125
4
8
Example 5
Writing a Repeating Decimal as a Fraction
To write 0.9 3 as a fraction, let x
0.9 3 .
Because 0.93 has 2 repeating digits, multiply each side of
1
2
x
0.93 by 10
, or 100. Then 100x
93.9 3 .
100x
93.9 3
Subtract x from 100x.
(x
0.9 3 )
2
99x
93
9
9
x
9
3
Solve for x and simplify.
3
9
9
9
9
3
1
x
3
3
3
1
Answer The decimal 0.93 is equivalent to the fraction
.
3
3
Checkpoint
Compare writing 0.3 as a fraction with writing 0.3
Critical Thinking
5.
as a fraction.
Example 6
Ordering Rational Numbers
5
5
1
3
Order the numbers
,
0.2, 4.31,
3,
,
from least to greatest.
4
2
3
Graph the numbers on a number line. You may want to write improper
fractions as mixed numbers.
Study Strategy
13
1
5
1
5
1
4
1
2
3
3
4
4
2
2
Another Way
To order the
numbers in Example 6, you
3
0.2
4.31
can instead write the fractions
0
1
2
3
4
5
5
4
3
2
1
as decimals. Then order the
decimals.
1
3
5
5
Read the numbers from left to right:
,
3,
,
0.2,
, 4.31.
3
4
2
221
Lesson 5.1
Rational Numbers
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