Convert the following repeating decimal to a fraction in simplest form.

Question

point, 6, start overline, 3, end overline
.6
3 3 a repeating

Answer 1

To convert the decimal .6 to a fraction, we can write it as 6/10, which simplifies to 3/5.

To represent the repeating decimal 3.3 (with the digit 3 repeating), we can use the formula for repeating decimals. Let x = 3.3. We can multiply both sides of the equation by a power of 10 to eliminate the repeating decimal:

10x = 33.3

Now, subtracting the original equation from the above equation:

10x - x = 33.3 - 3.3
9x = 30
x = 30/9
x = 10/3

Therefore, the repeating decimal 3.3 can be represented as the fraction 10/3.