Convert the following repeating decimal to a fraction in simplest form.
.96 ̅
To convert the repeating decimal .96̅ to a fraction, let's call the decimal x.
We can multiply x by 100 to eliminate the repeating decimal:
100x = 96.96̅
Next, we subtract x from 100x:
100x - x = 96.96̅ - .96̅
This simplifies to:
99x = 96
To isolate x, we divide both sides of the equation by 99:
x = 96 / 99
The fraction 96/99 can be simplified by finding the greatest common divisor (GCD) of 96 and 99, which is 3:
96 / 99 = (96 / 3) / (99 / 3) = 32 / 33
Therefore, the fraction equivalent to the repeating decimal .96̅ is 32/33 in simplest form.
To convert the repeating decimal .96 ̅ to a fraction in simplest form, we can use the formula for converting repeating decimals to fractions.
Let's represent the repeating decimal as "x" for simplicity.
1. Multiply the repeating decimal by a power of 10 that shifts the repeating part to the left of the decimal point:
100x = 96.96 ̅
2. Subtract the original repeating decimal from the shifted decimal to eliminate the repeating part:
100x - x = 96.96 ̅ - 0.96 ̅
99x = 96
3. Divide both sides of the equation by the non-repeating part of the repeating decimal (99 in this case):
x = 96 / 99
4. Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator, and dividing both by it:
GCD(96, 99) = 3
x = 32 / 33
Therefore, the fraction equivalent to .96 ̅ is 32/33 in simplest form.
To convert the repeating decimal .96̅ to a fraction in simplest form, we need to follow these steps:
Step 1: Identify the repeating pattern.
To express the repeating decimal .96̅ as a fraction, we need to first identify the repeating pattern. The bar above 96 indicates that the digits 9 and 6 repeat indefinitely.
Step 2: Create an equation.
Let x be the repeating decimal .96̅. To convert it to a fraction, we need to remove the repeating part by subtracting it. We can do this by multiplying x by a power of 10 that will shift the decimal point to the right before the repeating part.
Multiply both sides of the equation x = .96̅ by 100 to eliminate the decimal places:
100x = 96.96̅
Step 3: Subtract the equation.
To eliminate the repeating part, subtract the original equation from the equation obtained after multiplying both sides by 100.
100x - x = 96.96̅ - .96̅
This simplifies to:
99x = 96
Step 4: Solve for x.
To solve for x, divide both sides of the equation by 99:
x = 96/99
Step 5: Simplify the fraction.
Now we have x = 96/99. To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD) until they cannot be divided further.
The GCD of 96 and 99 is 3.
Dividing 96 by 3 gives us 32, and dividing 99 by 3 gives us 33:
x = 32/33
Therefore, the simplest form of the repeating decimal .96̅ is 32/33.