5/32 as a Decimal

Step-by-step solution

The problem

1. Divide 5 by 32 (long division). Write down how many times 32 goes in, carry the remainder, add a 0 and divide again. The remainder is 0, so the decimal ends here.

   Step	Divide	Digit	Remainder	Working
   Whole part	5 ÷ 32	0	5	32 × 0 = 0, 5 − 0 = 5
   Decimal place 1	50 ÷ 32	1	18	32 × 1 = 32, 50 − 32 = 18
   Decimal place 2	180 ÷ 32	5	20	32 × 5 = 160, 180 − 160 = 20
   Decimal place 3	200 ÷ 32	6	8	32 × 6 = 192, 200 − 192 = 8
   Decimal place 4	80 ÷ 32	2	16	32 × 2 = 64, 80 − 64 = 16
   Decimal place 5	160 ÷ 32	5	0	32 × 5 = 160, 160 − 160 = 0

2. Read off the decimal. The digits are read from the Digit column.

   = 5 \div 32 = \textcolor{#0b5c56}{0.15625}

3. Check with a shortcut. The denominator 32 can be made 100,000 by multiplying by 3125, so the decimal ends after 5 places.

   \frac{5}{32} = \frac{5 \times 3125}{32 \times 3125} = \frac{15{,}625}{100{,}000} = 0.15625

All the working together