23.6 repeating
find fraction notation
Surely you know that 2/3 = 0.6666666666
So, 23.6666 = 23 2/3
To find the fraction notation for the decimal 23.6 repeating, we can use the concept of repeating decimals. The repeating part in this case is 6, which means that there is an infinite string of 6s after the decimal point.
Step 1: Let x be the repeating decimal, so x = 23.6666...
Step 2: Multiply both sides of the equation by 10 to shift the decimal point one place to the right:
10x = 236.6666...
Step 3: Subtract the original equation from the multiplied equation to eliminate the repeating part:
10x - x = 236.6666... - 23.6666...
Simplifying both sides, we have:
9x = 213
Step 4: Solve for x by dividing both sides by 9:
x = 213 / 9
By dividing 213 by 9, we get x = 23.6 as the fraction notation for the repeating decimal 23.6 repeating.