How you would convert the repeating, nonterminating decimal to a fraction? Explain the process as you solve the problem. 0.1515 . . .
To convert the repeating, nonterminating decimal 0.1515... to a fraction, we can first observe that the decimal part "15" repeats indefinitely. To represent a repeating decimal as a fraction, we can use the concept of geometric series.
Let x = 0.1515...
Multiplying x by 100 to shift the decimal two places:
100x = 15.1515...
Now, subtract the initial equation from the second equation to eliminate the repeating part:
100x - x = 15.1515... - 0.1515...
99x = 15
Now, we can solve for x by dividing both sides of the equation by 99:
99x/99 = 15/99
x = 15/99
Simplifying the fraction by dividing the numerator and denominator by their greatest common divisor (which is 3):
x = 5/33
Therefore, the repeating decimal 0.1515... is equivalent to the fraction 5/33.
To convert the repeating, nonterminating decimal 0.1515... to a fraction, follow these steps:
Step 1: Let x be the decimal you want to convert to a fraction.
x = 0.1515...
Step 2: Multiply both sides of the equation by a power of 10 to shift the decimal point to the right.
10x = 15.1515...
Step 3: Subtract the original equation from the shifted equation, then solve for x.
10x - x = 15.1515... - 0.1515...
9x = 15
Step 4: Divide both sides of the equation by 9 to isolate x.
9x/9 = 15/9
x = 15/9
Step 5: Simplify the fraction, if possible.
Since 15 and 9 are both divisible by 3, we can simplify the fraction further.
x = 5/3
Therefore, the fraction equivalent of the repeating, nonterminating decimal 0.1515... is 5/3.