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| Decimal Fraction Conversion |
For repeating decimals:
0.33333333... = 3/9
0.73737373... = 73/99
0.174174174... = 174/999
Division by 9's causes the repeating pattern.
If zeros preceed the repeating decimal:
0.033333333... = 3/90
0.00073737373... = 73/99000
0.00174174174... = 174/99900
Zeros in the denominator correspond to zeros before the repeating decimal.
To convert a decimal that begins with a non-repeating part:
For example, to convert the number 0.21456456456456456... to a fraction, write it as the sum of the non-repeating part and the repeating part.
0.21 + 0.00456456456456456...
Next, convert each of these decimals to fractions. The first decimal has a divisor of power ten. The second decimal (which repeats) is converted according to the pattern above.
21/100 + 456/99900
Common denominators
20979/99900 + 456/99900
Sum
21435/99900
Simplify
1429/6660 = 0.2145645645...
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The material and content of Engineering Archives is designed to be subject to change and alteration at all times. Therefore, it may not be assumed that any presented material herein is static. The material is constantly subject to change for the purpose of maximizing the ability of the learner to comprehend and absorb the material. The changing and alteration is conducted based on user feedback. Therefore, effective changes cannot take place without the user feedback. Please go to the forum for questions and feedback. See more…
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