What is the fraction for the following decimal expansion?
0.16 repeating
answers
1/8
1/7
1/6
1/9
The fraction for the decimal expansion 0.16 repeating is 1/6.
To convert a decimal into fraction form, we can follow these steps:
Step 1: Let x represent the repeating decimal.
Step 2: Multiply both sides of the equation x = 0.16 repeating by a power of 10 to eliminate the repeating part. In this case, we need to multiply by 100 because there are two digits in the repeating part (16).
So, 100x = 16.16 repeating.
Step 3: Subtract the original equation from the equation obtained in Step 2.
100x - x = 16.16 repeating - 0.16 repeating.
Simplifying, we get: 99x = 16.
Step 4: Divide both sides by 99 to solve for "x."
x = 16/99.
Therefore, the fraction for the decimal expansion 0.16 repeating is 16/99.
To find the fraction equivalent of the repeating decimal 0.16, we need to convert it into a fraction. Here's how you can do it:
Step 1: Let x = 0.16 (the repeating decimal)
Step 2: Multiply both sides of the equation by 100 (to eliminate the decimal point):
100x = 16.16 (since 0.16 multiplied by 100 is 16.16)
Step 3: Subtract x from both sides of the equation:
100x - x = 16.16 - 0.16
99x = 16 (simplifying the equation)
Step 4: Divide both sides of the equation by 99 to isolate x:
x = 16/99
Therefore, the fraction equivalent of the repeating decimal 0.16 is 16/99.