what is .69 repeating in its simplest form? I need help
x = 0.6969...
100 x = 0.6969... * 100 = 69.6969...
100 x - x = 99 x = 69.6969... - 0.6969... = 69
99 x = 69
3 * 33 x = 3 * 23 Divide both sides by 3
33 x = 23 Divide both sides by 33
x = 23 / 33
0.6969... = 23 / 33
thx
To express a repeating decimal in its simplest form, we need to convert it into a fraction. In this case, we want to convert the repeating decimal .69 (with the 69 repeating) into a fraction.
Let x = .69 (with the 69 repeating).
Step 1: Multiply both sides of the equation by 100 to eliminate the decimal point:
100x = 69.6969...
Step 2: Subtract the original equation from the equation obtained in step 1 to eliminate the repeating decimals:
100x - x = 69.6969... - .69
Simplifying the equation, we get:
99x = 69
Divide both sides of the equation by 99:
x = 69/99
Now we have the fraction 69/99. To simplify this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 3:
69/99 = (69 ÷ 3) / (99 ÷ 3) = 23/33
Therefore, .69 repeating in its simplest form is 23/33.