Real Numbers And The Pythagorean Theorem Worksheet - Chapter 7 Page 31
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46Writing a Repeating Decimal as a Fraction (1 Digit Repeats)
2 2
EXAMPLE
—
Write −0.2
3 as a fraction in simplest form.
—
Let x = − 0.2
3 .
—
x = − 0.2
3
Step 1: Write the equation.
⋅
⋅
—
Step 2: There is 1 repeating digit, so multiply
x = 10
Check
10
(− 0.2
3 )
1
each side by 10
= 10.
—
10x = − 2.
3
Simplify.
—
− (x = − 0.2
3 )
Step 3: Subtract the original equation.
9x = − 2.1
Simplify.
− 2.1
x =
—
Step 4: Solve for x.
9
− 2.1
—
21
7
So, − 0.2
3 =
= −
= −
—
—
—
.
9
90
30
3 3
Writing a Repeating Decimal as a Fraction (2 Digits Repeat)
EXAMPLE
—
Write 1.
25 as a mixed number.
—
Let x = 1.
25 .
—
x = 1.
25
Step 1: Write the equation.
⋅
⋅
—
Step 2: There are 2 repeating digits, so multiply
x = 100
Check
100
1.
25
2
each side by 10
= 100.
—
100x = 125.
25
Simplify.
—
− (x =
1.
25 )
Step 3: Subtract the original equation.
99x = 124
Simplify.
124
x =
—
Step 4: Solve for x.
99
—
124
25
25 =
= 1
—
—
So, 1.
.
99
99
Write the decimal as a fraction or a mixed number.
—
—
—
—
7. − 0.4
10. − 4.
3
8. 2.0
6
9. 0.
27
50
REPEATED REASONING
Find a pattern in the fractional representations of repeating
11.
decimals in which only the tenths and hundredths digits repeat. Use the pattern to
—
explain how to write 9.
04 as a mixed number.
Extension 7.4
Repeating Decimals
317
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