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There are certain shortcuts, but here is the general idea. For example, convert 0.4121212... to a fraction. Call this number "x", and write:
x = 0.4121212...
Multiply this equation by 100, in this case, because two digits repeat; if three digits repeat, multiply by 1000, etc. Write the equations one below the other, as follows:
100x = 41.21212...
x = 0.4121212...
Now subtract one equation from the other:
99x = 40.8
Solve for x:
x = 40.8 / 99 = 408 / 990
Simplify the answer.
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Is a repeating decimal rational?
yes, repeating decimals (those that have infinite - never ending - number of digits after the decimal point and these decimals show repeating pattern) are rational numbers, because they can be written as fractions.
Is a rational number a repeating decimal?
All repeating decimals are rational numbers. Not all rational numbers are repeating decimals.
How do you turn fractions into decimals and example?
To turn improper and proper fractions to decimals, divide the numerator by the denominator. Examples: 1. 27/10 = 27 ÷ 10 = 2.7 2. 11/36 = 11 ÷ 36 = 0.3055 To turn mixed fractions to decimals, add the whole number to the quotient of the proper fraction. 6 1/8 = 6 + (1 ÷ 8) = 6 + 0.125 = 6.125
Can all terminating decimals be written as fractions?
All terminating decimals can be written as fractions.
What is a positive number with no decimals or fractions?
Whole numbers are positive numbers and there are no fractions or decimals.
