What is 7 and 6/13 as a Decimal?

Fraction to Decimal Converter

What is 7 6/13 as a decimal?

Answer

Fraction 7 6/13 as a decimal is

7.461538

≈ 7.46 to hundredths

Repeating decimal: denominator 13 has the factor 13, not 2 or 5 · the bar marks the period 461538 — 6 digits repeat forever

Whole part 7 stays in front; divide the fraction part:

remainder	×10	= digit × 13 + new remainder	digit
6	60	4 × 13 + 8	4
8	80	6 × 13 + 2	6
2	20	1 × 13 + 7	1
7	70	5 × 13 + 5	5
5	50	3 × 13 + 11	3
11	110	8 × 13 + 6	8

Remainder 6 is back after the 6th division → the 6 digits 461538 repeat: 0.461538.

7 + 0.461538 = 7.461538

Fraction 7 6/13 as a decimal is 7.(461538)

To convert 7 6/13 to a decimal, divide the numerator by the denominator, 6 ÷ 13 = 0.(461538), then add the whole part: 7 + 0.(461538) = 7.(461538).

In lowest terms its denominator 13 has the prime factor 13, so the division never ends: a remainder comes back and the same digits repeat forever.

Multiply by 100: 7 6/13 ≈ 746.15%.