Question

A numeral system or system of numeration is the writing system for
expressing numbers. Let's play with numbers/ digits and record our
observations.
Write down counting numbers from 1 to 20 in an order. You will observe that
you
have written 31 digits in all as numbers from 10 to 20 contain 2 digits numbers
also.
Can you find the number of digits for counting numbers from 1 to 1000.
• Further, if 1000 digits were written in total how many
complete numbers
(1- digit, 2- digit, 3- digit etc) would be written down?​

Answer 1

Given :  Write down counting numbers from 1 to 20 in an order.  written 31 digits in all as numbers

To Find :   the number of digits for counting numbers from 1 to 1000.

If 1000 digits were written in total how many complete numbers

(1- digit, 2- digit, 3- digit etc) would be written down?​

Solution:

1 to 9  - 1 Digit  hence digits used  = 9 * 1 = 9

10 to 99   2 Digit  Hence digits used = 90 * 2 = 180

100 to 999 3 Digits hence Digits uses = 900 * 3 = 2700

1000 = 4 Digits

9 + 180 + 2700 + 4

= 2893  Digits used

1000 digits were written

1 Digit number   = 9    

2 Digit Number = 90

Digits remaining  = 1000  -  9  - 180

= 811

811 = 270 * 3 + 1  

270  Complete 3 Digits numbers

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