how do you convert

.466666666666 repeating to a fraction

47/100

467/1000
4667/10,000

and so on

To convert the repeating decimal .466666666 to a fraction, you can follow these steps:

Step 1: Let x = .466666666...
Step 2: Multiply both sides of the equation by 10 to remove the repeating decimal:
10x = 4.666666666...
Step 3: Subtract the original equation from the equation obtained in step 2:
10x - x = 4.666666666... - .466666666...
Simplifying this equation, we get:
9x = 4.2
Step 4: Divide both sides of the equation by 9 to solve for x:
x = 4.2 / 9
So, the fraction representation of the repeating decimal .466666666... is 4.2 / 9.

To convert a repeating decimal to a fraction, you need to understand the concept of repeating decimals and use algebraic manipulation. Let's consider the decimal .466666666666, where 6 repeats infinitely.

Step 1: Assign a variable to the repeating part of the decimal.
Let x = .466666666666...

Step 2: Multiply both sides of the equation by a power of 10 to shift the decimal point to the right of the repeating part.
10x = 4.66666666666...

Step 3: Subtract the original equation from the shifted equation to eliminate the repeating part.
10x - x = 4.66666666666... - 0.46666666666...
This simplifies to:
9x = 4.2

Step 4: Solve for x by dividing both sides of the equation by 9.
9x/9 = 4.2/9
x = 4.2/9

Therefore, the fraction equivalent of the repeating decimal .466666666666 is 4.2/9.