What is the repeating decimal 0.282282282 as a fraction in simplest form?
141141141/5000000000*
multiply by 1000 to move the decimal point three places for three digit repeat
n = 0.282282282...
1000 n = 282.282282...
subtract ... 999 n = 282
divide ... n = 282/999
Thanks
To express the repeating decimal 0.282282282 as a fraction in simplest form, we need to understand that the digits 282 repeat indefinitely. To solve this, we can use algebra.
Let's represent the repeating decimal as x:
x = 0.282282282...
Now, we can multiply both sides of the equation by 1000, since there are 3 decimal places:
1000x = 282.282282...
Next, let's subtract x from 1000x to eliminate the repeating part:
1000x - x = 282.282282... - 0.282282282...
This simplifies to:
999x = 282
To isolate x, we divide both sides of the equation by 999:
x = 282/999
Now we can simplify the fraction by finding the greatest common divisor (GCD) of the numerator (282) and the denominator (999). In this case, the GCD is 3, so we can divide both numerator and denominator by 3:
282 ÷ 3 = 94
999 ÷ 3 = 333
Therefore, the simplified fraction form of the repeating decimal 0.282282282 is:
94/333