What is 5 and 10/7 as a Decimal?

Fraction to Decimal Converter

What is 5 10/7 as a decimal?

Answer

Fraction 5 10/7 as a decimal is

6.428571

≈ 6.43 to hundredths

Repeating decimal: denominator 7 has the factor 7, not 2 or 5 · the bar marks the period 428571 — 6 digits repeat forever

10 = 1 × 7 + 3: whole part 5 + 1 = 6, then divide the remainder 3

remainder	×10	= digit × 7 + new remainder	digit
3	30	4 × 7 + 2	4
2	20	2 × 7 + 6	2
6	60	8 × 7 + 4	8
4	40	5 × 7 + 5	5
5	50	7 × 7 + 1	7
1	10	1 × 7 + 3	1

Remainder 3 is back after the 6th division → the 6 digits 428571 repeat: 0.428571.

6 + 0.428571 = 6.428571

Fraction 5 10/7 as a decimal is 6.(428571)

To convert 5 10/7 to a decimal, divide the numerator by the denominator, 10 ÷ 7 = 1.(428571), then add the whole part: 5 + 1.(428571) = 6.(428571).

In lowest terms its denominator 7 has the prime factor 7, so the division never ends: a remainder comes back and the same digits repeat forever.

Multiply by 100: 5 10/7 ≈ 642.86%.