Question

How many times does the digit 6 appear in the first 1000 natural numbers?

Answer 1

How many times does the digit 6 appear in the first 1000 natural numbers is109

Answer 2

Answer:

Total 300 times the digit 6 appear in the first 1000 natural number.

Step-by-step explanation:

Number of 6 from 1 to 100 are 6, 16, 26, 36, 46, 56, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 76, 86, 96

Total number of 6 from 1 to 100 $= 20$ (66 has 2 6's)

Same pattern will follow for every set of 100 numbers upto 100 like 200 to 300, 300 to 400

But we have to include number of 6 from 600 to 699 also which are 100 in number

So,

Total number of 6 from 1 to 1000 = 20 × 10 + 100

$1000 = 20 \times 10 + 100 \\ = 200 + 100 \\ = 300$

Therefore,total 300 times the digit 6 appear in the first 1000 natural number.

This is a problem of Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549