Convert the following, repeating, decimal to a fraction in simplest form ≈.17
To convert the repeating decimal ≈ 0.17 to a fraction in simplest form, we'll assign a variable to the decimal and solve for it.
Let x = 0.17
Multiply both sides by 100 to move the decimal point two places to the right:
100x = 17
Subtract x from both sides:
100x - x = 17 - 0.17
99x = 16.83
To remove the decimal point, we multiply both sides by 100:
(99x)(100) = 16.83(100)
9900x = 1683
Divide both sides by 9900:
x = 1683/9900
Now, simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3:
x = (561/3300)
The fraction 561/3300 is the simplest form of the repeating decimal 0.17 ≈ 561/3300.