A number with 100 digits is given. The first two digits of that number are 2 and 9.How many digits has a square of that number? About the author Rose
Step-by-step explanation: Given:– A number with 100 digits is given. The first two digits of that number are 2 and 9. To find:– How many digits has a square of that number? Solution:– Number of digits in the given number = 100 The first two digits in the number = 2 and 9 Wr know that The number of digits in the square of a number with one digit (from 1-9) = 1 or 2 since 1^2=1 and 9^2=81 The number of digits in the square of a number with two digits (from 10-99)= 3 or 4 Since 10^2 = 100 and 99^2 = 9801 The number of digits in the square of a number with three digits (from 100-999)= 4 or 5 If we continue like this we get the following general formula: 1 or 2 can be written as 2(1)-1 or 2(1) 3 or 4 can be written as 2(2)-1 or 2(2) 5 or 6 can be written as 2(3)-1 or 2(3) . . . The number of digits in the square of a number with n digits =2n-1 or 2n So , The number of digits in the square of a number with 100 digits = 2(100)-1 or 2(100) =>200-1 or 200 =>199 or 200 If it has 2 in its units place it has 199 digits in the square of the number. If it has 9 in its units place it has 200 digits in the square of the number. Answer:– The number of digits in the square of a number with 100 digits = 199 or 200 1)If it has 2 in its units place it has 199 digits in the square of the number. (The first two digits like 29) 2)If it has 9 in its units place it has 200 digits in the square of the number. (The first two digits like 92) Used formulae:– The number of digits in the square of a number with n digits =2n-1 or 2n Reply
Given : a number with 100 digits The first two digits of that number are 2 and 9 To Find : How many digits has a square of that number 29yyyy________ Hence its less than 300000_________ 3 with 99 0’s and greater than 2000000_______ 2 with 99 0’s Square of 3 with 99 0’s will be 9000000_______ 9 with 198 0’s Hence 199 digits Square of 2 with 99 0’s will be 4000000_______ 4 with 198 0’s Hence 199 digits Hence square of that number is greater than a number of 199 digits also lesser than a number of 199 digits Hence number must be of 199 digits so square of that number will have 199 Digits Learn More: By mere observation, find the number ofdigits in the square roots of … brainly.in/question/9884489 EXERCISE 3.41. Find the number of digits in the square roots of the … brainly.in/question/20071362 Reply
Step-by-step explanation:
Given:–
A number with 100 digits is given. The first two digits of that number are 2 and 9.
To find:–
How many digits has a square of that number?
Solution:–
Number of digits in the given number = 100
The first two digits in the number = 2 and 9
Wr know that
The number of digits in the square of a number with one digit (from 1-9) = 1 or 2
since 1^2=1 and 9^2=81
The number of digits in the square of a number with two digits (from 10-99)= 3 or 4
Since 10^2 = 100 and 99^2 = 9801
The number of digits in the square of a number with three digits (from 100-999)= 4 or 5
If we continue like this we get the following general formula:
1 or 2 can be written as 2(1)-1 or 2(1)
3 or 4 can be written as 2(2)-1 or 2(2)
5 or 6 can be written as 2(3)-1 or 2(3)
.
.
.
The number of digits in the square of a number with n digits =2n-1 or 2n
So ,
The number of digits in the square of a number with 100 digits =
2(100)-1 or 2(100)
=>200-1 or 200
=>199 or 200
If it has 2 in its units place it has 199 digits in the square of the number.
If it has 9 in its units place it has 200 digits in the square of the number.
Answer:–
The number of digits in the square of a number with 100 digits = 199 or 200
1)If it has 2 in its units place it has 199 digits in the square of the number.
(The first two digits like 29)
2)If it has 9 in its units place it has 200 digits in the square of the number.
(The first two digits like 92)
Used formulae:–
Given : a number with 100 digits
The first two digits of that number are 2 and 9
To Find : How many digits has a square of that number
29yyyy________
Hence its less than
300000_________
3 with 99 0’s
and greater than
2000000_______
2 with 99 0’s
Square of 3 with 99 0’s will be
9000000_______
9 with 198 0’s
Hence 199 digits
Square of 2 with 99 0’s will be
4000000_______
4 with 198 0’s
Hence 199 digits
Hence square of that number
is greater than a number of 199 digits also lesser than a number of 199 digits
Hence number must be of 199 digits
so square of that number will have 199 Digits
Learn More:
By mere observation, find the number ofdigits in the square roots of …
brainly.in/question/9884489
EXERCISE 3.41. Find the number of digits in the square roots of the …
brainly.in/question/20071362