Sum of Digits

Number Theory Level 2

Find the sum of the digits of the integer 1 0 999 10^{999} - 5 .


The answer is 8987.

John Paolo Bayaborda by John Paolo Bayaborda , 24, Philippines

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4 solutions

10 is raised to 999, therefore, it has 1000 digits, right? If we subtract 5 from it, there will only be 999 digits. And we know that the ones digit of this integer is 5 and the remaining 998 digits is 9. So, 998 x 9 +5 = 8987

4 Helpful 0 Interesting 0 Brilliant 0 Confused

10^x-5=9(x-1)+5 and hence the ans will be 8987,as our x is 999

Abhilasha Choudhary - 7 years, 1 month ago
Mahdi Raza
Jun 12, 2020

1 0 999 − 5 = 999 … 999 ⏟ 998 times 5 10^{999} - 5 = \underbrace{999 \ldots 999}_{\text{998 times}} 5

Digit sum is: 9 × 998 + 5 = 8987 9 \times 998 + 5 = \boxed{8987}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Pavita Ardhani
Apr 28, 2014

(999-1) x 9 = 8982 (sum of 9's) + 5 = 8987

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Pratik Ranjan
Apr 30, 2014

10 to the power x means after 1 there will be x number of zeroes .. so 10 to the power 999 means after 1 there will be 999 zeroes .. now subtracting 5 from zero at units place ... by taking carry .. we get 5 at units place and 998 number of 9 in rest place .. so sum of digits =9*998+5=8987

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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