What is 5/6 turned into a decimal
The Correct Answer and Explanation is:
Answer:
56=0.833333…\displaystyle \frac56 = 0.833333\ldots (the 3 repeats forever).
explanation
Converting 5⁄65⁄6 to a decimal asks how many tenths, hundredths, thousandths, and so on equal the same slice of a whole that five sixths represents. Long-division, which repeatedly subtracts multiples of the divisor while keeping track of place value, supplies a dependable route from fraction to decimal.
Begin by writing 6 (the divisor) outside the bracket and 5 (the dividend) inside. Because 6 exceeds 5, place 0. in the quotient and tack a zero onto the dividend, making 50. Six fits into 50 eight times, because 8×6=488 × 6 = 48. Record the 8, subtract, and two remains. Drop another zero to produce 20. Six fits into 20 three times (3×6=183 × 6 = 18), again leaving remainder 2. Each repetition—append zero, divide, subtract—restores that same remainder, so another 3 joins the quotient every cycle. The digits after the initial 8 therefore read 3, 3, 3, continuing forever; the exact decimal is 0.833333…0.833333\ldots.
Why does the stream of 3’s never end? A rational number yields a terminating decimal only when, after simplification, its denominator is built solely from the primes 2 and 5, because powers of ten are 2n5n2^n5^n. The denominator 6 factors as 2×32 × 3. The lone factor 3 cannot be balanced by any power of ten, so the remainder can never collapse to zero. Instead, it loops back to 2 after one step, giving a repeating block (called the period) of length 1.
Mathematicians indicate the endlessly repeating digit by writing 0.83‾0.8\overline{3} (a bar over the 3). Any finite display—0.83, 0.833, 0.8333—is merely a rounded snapshot; multiplying that rounded value can introduce small cumulative errors. The issue surfaces in compound-interest forecasts, mortgage amortizations, engineering tolerance charts, and statistical sampling design. Recognizing the repeat alerts you to hidden approximation and error.
