How you would convert the repeating, nonterminating decimal to a fraction? 0.1515
Plss help
100x = 15.1515...
x = 0.1515...
subtract and you have
99x = 15
x = 15/99 = 5/33
In general, if you have n digits repeating (0.xxxx) the fraction is just the repeating digits over the same number of 9's.
0.143143143... = 143/999
I meant how you could sorry :}
To convert the repeating, nonterminating decimal 0.1515 to a fraction, you can use the following steps:
Step 1: Let x = 0.1515
Step 2: Multiply both sides of the equation by 10000 to remove the decimal point:
10000x = 1515.1515
Step 3: Subtract the equation in step 1 from the equation in step 2:
10000x - x = 1515.1515 - 0.1515
9975x = 1515
Step 4: Simplify the equation by dividing both sides by 9975:
x = 1515/9975
Step 5: Simplify the fraction 1515/9975 by finding the greatest common divisor (GCD) of both numerator and denominator, and dividing them by it:
GCD(1515, 9975) = 45
1515/45 = 337
9975/45 = 221
Step 6: Therefore, the repeating decimal 0.1515 can be expressed as a fraction 337/221.
To convert a repeating, nonterminating decimal to a fraction, you need to understand the concept of a repeating decimal and use algebraic manipulation.
To convert the repeating decimal 0.1515 to a fraction, we will create an equation to eliminate the repeating part. Let's call the unknown fraction x:
Step 1: Multiply the decimal by a power of 10 to eliminate the repeating part.
100x = 15.1515 (Multiply both sides of the equation by 100 since there are two digits repeating)
Step 2: Subtract the original equation from Step 1.
100x - x = 15.1515 - 0.1515 (Subtract 0.1515 from both sides of the equation)
Simplifying the equation:
99x = 15
Step 3: Solve for x by dividing both sides of the equation by 99.
x = 15/99
The fraction 15/99 is the simplified form of the repeating decimal 0.1515.