Question

Raju wanted to type the first 180 natural numbers . find the number of times he had to press the number keys?​

Answer 1

Question :-- Raju wanted to type the first 180 natural numbers . find the number of times he had to press the number keys ?

Answer :-

There are 9 one digit natural numbers that are 1 to 9 = 9

And , we know that Number of digits in the natural numbers 1 to 9 = 1

So,

→ Number of times the key will be pressed = 9 × 1 = 9 ------ Equation (1)

____________________________

Now , Number of two digit numbers : 10 to 99 = 90

Number of digits in the natural numbers from 10 to 99 = 2

So,

→ number of times the key will be pressed to type the two digit numbers = 90 × 2 = 180 ------ Equation (2)

____________________________

Number of three digit numbers : 100 to 180 = 81

Number of digits in the natural numbers from 100 to 180 = 3

So,

→ number of times the key will be pressed to type the three digit numbers = 81 × 3 = 243. ----- Equation (3)

_____________________

Adding Equation (1), (2), and (3) now, we get,

→ Total number of times the key will be pressed = 9 + 180 + 243 = 432 .

Hence, Raju had to Press 432 times the number To write Natural Numbers upto 180.

Answer 2

$\huge\underline{\underline{\bf \orange{Question-}}}$

Raju wanted to type the first 180 natural numbers .Find the number of times he had to press the number keys ?

$\huge\underline{\underline{\bf \orange{Solution-}}}$

$\large\underline{\underline{\sf Given:}}$

• Raju wanted to type the first 180 natural numbers.

$\large\underline{\underline{\sf To\:Find:}}$

• Find the number of times he had to press the number keys.

______________________________________

One digit natural numbers are ⎯

➝ 1 to 9

➝9

Number of times key pressed ⎯

➝9 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎯ (1)

Two digit natural numbers are ⎯

➝ 10 to 99

➝ 90

Number of times key pressed ⎯

➝ 90 × 2

➝ 180 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎯ (2)

Three digit natural numbers are ⎯

➝ 100 to 180

➝ 81

Number of times key pressed ⎯

➝ 81 × 3

➝ 243 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎯ (3)

From Equation 1 , 2 and 3

$\implies{\sf 9+180+243}$

$\implies{\bf \red{ 432 }}$

$\huge\underline{\underline{\bf \orange{Answer-}}}$

Number of times Raju had to press the number key is ${\bf \red{432}}$