Convert the repeating decimal 0.333... to a fraction.

Convert the repeating decimal 0.333... to a fraction.

• A. 1/6
• B. 1/3
• C. 2/3
• D. 3/8

Answer: (B)

A repeating decimal can be written as a fraction by turning it into an equation. Let x be the decimal 0.333... Then multiplying by 10 shifts the repeating part: 10x = 3.333.... Subtracting the original x cancels the repeating part: 10x − x = 9x = 3, so x = 3/9 = 1/3. Therefore 0.333... equals 1/3. For quick checks, 1/6 equals 0.1666..., 2/3 equals 0.6666..., and 3/8 equals 0.375, none of which match the repeating 0.333....

A repeating decimal can be written as a fraction by turning it into an equation. Let x be the decimal 0.333... Then multiplying by 10 shifts the repeating part: 10x = 3.333.... Subtracting the original x cancels the repeating part: 10x − x = 9x = 3, so x = 3/9 = 1/3. Therefore 0.333... equals 1/3.

For quick checks, 1/6 equals 0.1666..., 2/3 equals 0.6666..., and 3/8 equals 0.375, none of which match the repeating 0.333....