Convert the following repeating decimal to a fraction simplest form
.32 ̅
To convert a repeating decimal to a fraction, we need to identify a pattern and create an equation to solve for the fraction value.
Let's denote the repeating decimal as x:
x = .32̅
To eliminate the repeated part, we can multiply x by 100 to shift the repeating part two digits to the left:
100x = 32.32̅
Now, subtract the original value of x from 100x:
100x - x = 32.32̅ - .32̅
99x = 32
To isolate x, divide both sides of the equation by 99:
x = 32/99
Therefore, the fraction equivalent of the repeating decimal .32̅ is 32/99.
To convert the repeating decimal .32̅ to a fraction in simplest form, you can follow these steps:
Step 1: Let x = .32̅ (this is the repeating decimal we want to convert).
Step 2: Multiply both sides of the equation by a power of 10 that would eliminate the repeating part. Since the decimal .32̅ has two digits in the repeating part, we'll multiply both sides by 100:
100x = 32.32̅
Step 3: Subtract x from 100x to eliminate the repeating part:
100x - x = 32.32̅ - .32̅
99x = 32
Step 4: Divide both sides of the equation by 99:
x = 32/99
Therefore, the repeated decimal .32̅ can be expressed as the fraction 32/99 in its simplest form.
To convert the repeating decimal .32̅ to a fraction in simplest form, we need to understand the concept of repeating decimals. A repeating decimal is a decimal in which one or more digits repeat infinitely. In this case, the number 32 repeats infinitely after the decimal point. To convert it to a fraction, we follow these steps:
Step 1: Assign the repeating decimal to the variable x.
x = .32̅
Step 2: Multiply the entire equation by 100 to eliminate the repeating part.
100x = 32.32̅
Step 3: Subtract the original equation from the equation in Step 2 to eliminate the repeating part.
100x - x = 32.32̅ - .32̅
99x = 32
Step 4: Solve for x by dividing both sides of the equation by 99.
x = 32/99
Therefore, the repeating decimal .32̅ can be written as the fraction 32/99 in simplest form.