63/64 as a Decimal

Step-by-step solution

The problem

1. Divide 63 by 64 (long division). Write down how many times 64 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	63 ÷ 64	0	63	64 × 0 = 0, 63 − 0 = 63
   Decimal place 1	630 ÷ 64	9	54	64 × 9 = 576, 630 − 576 = 54
   Decimal place 2	540 ÷ 64	8	28	64 × 8 = 512, 540 − 512 = 28
   Decimal place 3	280 ÷ 64	4	24	64 × 4 = 256, 280 − 256 = 24
   Decimal place 4	240 ÷ 64	3	48	64 × 3 = 192, 240 − 192 = 48
   Decimal place 5	480 ÷ 64	7	32	64 × 7 = 448, 480 − 448 = 32
   Decimal place 6	320 ÷ 64	5	0	64 × 5 = 320, 320 − 320 = 0

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

   = 63 \div 64 = \textcolor{#0b5c56}{0.984375}

3. Check with a shortcut. The denominator 64 can be made 1,000,000 by multiplying by 15,625, so the decimal ends after 6 places.

   \frac{63}{64} = \frac{63 \times 15{,}625}{64 \times 15{,}625} = \frac{984{,}375}{1{,}000{,}000} = 0.984375

All the working together