Give-the-result-of-the-following-computation-as-an-integer-in-the-usual-decimal-form-303-000-000-000-303-3-300-000-033-1-000-100-010-001-

Question Number 518 by Yugi last updated on 25/Jan/15

G i v e t h e r e s u l t o f t h e f o l l o w i n g c o m p u t a t i o n a s a n i n t e g e r i n t h e u s u a l d e c i m a l

f o r m .

\frac{303, 000, 000, 000, 303 \times 3, 300, 000, 033}{1, 000, 100, 010, 001}

Answered by prakash jain last updated on 22/Jan/15

\frac{303 (10^{12} + 1) \times 33 \times (10^{8} + 1)}{(10^{12} + 10^{8} + 10^{4} + 1)}

= \frac{303 \times 33 \times (10^{12} + 1) (10^{8} + 1)}{[10^{8} (10^{4} + 1) + (10^{4} + 1)]}

= \frac{303 \times 33 \times [{(10^{4})}^{3} + 1] [10^{8} + 1]}{(10^{8} + 1) (10^{4} + 1)}

= \frac{303 \times 33 (10^{4} + 1) (10^{8} - 10^{4} + 1)}{10^{4} + 1}

= 303 \times 33 \times (10^{8} - 10^{4} + 1)

= 9999 \times (99990000 + 1)

= 9999 \times 9999 \times 10000 + 9999

= {(10000 - 1)}^{2} \times 10000 + 9999

= (100000000 - 20000 + 1) \times 10000 + 9999

= (99980000 + 1) \times 10000 + 9999

= 999800010000 + 9999

= 999800019999