Name _______________________________________
Date __________________
Hour ___________
Problem 4.3 Representing Decimals as Fractions
Focus Question: Can you represent every repeating or terminating decimal as a fraction?
A. 1. In the table below, write each fraction as a decimal.
Fraction
Decimal
Fraction
1
9
2
9
3
9
4
9
5
9
6
9
7
9
Decimal
1
11
2
11
3
11
4
11
5
11
6
11
7
11
2. Describe any patterns you see in your table.
B. Use the patterns you found in Question A to write a decimal representation for each rational
number. Use your calculator to check your work.
1.
9
9
2. −
10
3.
9
10
11
4.
−12
11
C. Find a fraction equivalent to each decimal, if possible.
1. 1.222 . . .
2. 2.777 . . .
3. 0.818181 . . .
4. 0.27277277727777 . . .
5. 1.99999
6. 0.99999 . . .
Looking For Pythagoras
Investigation 4: Using The Pythagorean Theorem: Understanding Real Numbers
D. The patterns from Question A can help you represent some repeating decimals as fractions. What
about other repeating decimals, such as 0.121212 . . .? You need a method that will help you find an
equivalent fraction for any repeating decimal.
1. Suppose 𝑥 = 0.121212 . . . What is 100𝑥?
Is it still a repeating decimal?
2. Complete the subtraction.
100𝑥 = 12.121212. ..
−
𝑥 = 0.121212 …
99𝑥 =
Is the answer for 99𝑥 still a repeating decimal?
3. Find a fraction form for 0.121212. . . by solving for 𝑥.
4. Why do you think this method starts out by multiplying by 100? Explain.
5. Use this method to write each repeating decimal as a fraction.
a. 0.151515. . .
b. 0.123123123. . .
E. Tell whether each statement is true or false.
1. You can write any fraction as a terminating or repeating decimal.
2. You can write any terminating or repeating decimal as a fraction.
Looking For Pythagoras
Investigation 4: Using The Pythagorean Theorem: Understanding Real Numbers