What is 3 and 8/7 as a Decimal?

Fraction to Decimal Converter

What is 3 8/7 as a decimal?

Answer

Fraction 3 8/7 as a decimal is

4.142857

≈ 4.14 to hundredths

Repeating decimal: denominator 7 has the factor 7, not 2 or 5 · the bar marks the period 142857 — 6 digits repeat forever

8 = 1 × 7 + 1: whole part 3 + 1 = 4, then divide the remainder 1

remainder	×10	= digit × 7 + new remainder	digit
1	10	1 × 7 + 3	1
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

Remainder 1 is back after the 6th division → the 6 digits 142857 repeat: 0.142857.

4 + 0.142857 = 4.142857

Fraction 3 8/7 as a decimal is 4.(142857)

To convert 3 8/7 to a decimal, divide the numerator by the denominator, 8 ÷ 7 = 1.(142857), then add the whole part: 3 + 1.(142857) = 4.(142857).

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: 3 8/7 ≈ 414.29%.