Download More Practice Converting Repeating Decimals to Rational Numbers

More Practice Converting
Repeating Decimals to Rational Numbers
Converting any repeating decimal into a rational number follows the following steps:
1. Count the number of digits under the repeat bar and set that number equal to x.
a. Example: 0.3 has one digit under the bar so x = 1
b. Example: 0. 36 has two digits under the bar so x = 2
c. Example: 0.00275 has three digits under the bar so x = 3
2. Multiply the original number by 10
3. 3
a. Example: 0. 3 10
36. 36
b. Example: 0. 36 10
c. Example: 0.00275 10
2.75275
3. Set the product obtained in step 2 equal to 10
a. Example: 3. 3 10
b. Example: 36. 36 100
c. Example: 2.75275 1000
4. Set the original number equal to n
a. Example: 0. 3
b. Example: 0. 36
c. Example: 0. 00275
5. Subtract the equation in step 4 from the equation in step 3
a. Example:
3. 3 10
0. 3 3 = 9n
b. Example:
36. 36 100
0. 36 36
= 99n
c. Example:
2.75275 1000
0.00275 2.75
= 999n
6. Solve for n
a. Example:
3 = 9n
b. Example:
c. Example:
36 = 99n
2.75 = 999n
100[2.75 = 999n]
275 = 99900n
Your turn:
Convert each of the following from the decimal form into the rational number form:
1.)
0. 6
2.)
3. 8
3.)
2. 09
4.)
2. 27
5.)
1. 58
6.)
3.0245
7.)
1.881
8.)
2.7819
9.)
0. 3591
10.)
1. 153846
Answer Key:
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