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Solutions for Session 7, Part B
See solutions for Problems: B1 | B2 | B3 | B4
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Problem B1 | |
a. | Since this is a terminating decimal, 0.125 = 125/1,000, which can be reduced to 1/8. |
b. | Use the method of multiplication. If F = 0.125125125..., then 1,000F = 125.125125125... Subtracting F from both sides gives you 999F = 125, so F = 125/999. |
<< back to Problem B1
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Problem B2 | |
a. | Since this is a terminating decimal, 0.5436 = 5,436/10,000 = 1,359/2,500. |
b. | F = 0.54365436.... Multiply by 10,000 to get 10,000F = 5,436.54365436.... Subtracting F from both sides gives you 9,999F = 5,436, so F = 5,436/9,999, which can be reduced to 604/1,111. |
<< back to Problem B2
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Problem B3 | |
a. | 0.236 = 236/1,000 = 59/250. |
b. | Note the difference; only the 36 is repeated! In this case, F = 0.2363636.... Multiply by 100 to get 100F = 23.6363636.... Subtracting F from both sides gives you 99F = 23.4, so F = 23.4/99, or 234/990, which can be reduced to 13/55. |
<< back to Problem B3
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Problem B4 | |
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Multiplying by 10 yields 10F = 1.111111.... Subtracting F from both sides gives you 9F = 1. Thus, F = 1/9. (It may seem counterintuitive at first that 0.11111111... = 1/9 since there are no 9s in the decimal!)
<< back to Problem B4
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