Shifting of Digits in a Number

What is the Effect of shifting of digits in a number?

Let us observe two numbers 1528 and 5182. We see that the digits are the same, but places are different in these two numbers. Thus, if the digits of a number are shifting or interchanged, the number also gets changed.

Working Rules

Step I: Obtain the new number from the given number by shifting/exchanging its digit.

Step II: Compare the new number with the given number.

1. If the digits 4 and 8 of 5408 are exchanged, then the new number so formed is

(i) greater than the original number.

(ii) 1253 more than the original number.

(iii) 5312 less than the original number.

(iv) Both (i) and (ii)

Solution:

If we exchange the places of 4 and 8 in 5408, we get 5804.

Now, let us compare 5408 and 5804.

Clearly, the new number 5804 is greater than the given number 5408.

So, the option (i) is correct, which is the required answer. 5408 5804

2. Shift the digit 5 towards right from its place in 5130 and compare the new numbers so formed with the given number.

Solution:

We can get the three new numbers from the number 5130 in the following three ways by shifting the digit 5 towards right from its place.

Since, all these numbers so formed have 1 in thousands place as compared to that of 5 in 5130, all these numbers are less than the given number 5130.

Worksheet on Shifting of Digits in a Number:

1. Exchange the digits 4 and 6 in the following numbers and compare the new numbers with the previous ones:

(i) 4896

(ii) 6247

(iii) 5654

Answer:

1. (i) 4896; Exchange the digits 4 and 6 = 6894; Therefore, 4896 < 6894

(ii) 6247; Exchange the digits 4 and 6 = 4267; Therefore, 6247 < 4267

(iii) 5654; Exchange the digits 4 and 6 = 5456; Therefore, 5654 > 5456

2. Shift the digit 3 towards right from its place and compare the new number with the previous ones:

(i) 3198

(ii) 7325

(iii) 4931

Answer:

2. (i) 3198; Shift the digit 3 towards right from its place = 1398;

         Therefore, 3198 > 1398

(ii) 7325; Shift the digit 3 towards right from its place = 7235;

         Therefore, 7325 > 7235

(iii) 4931; Shift the digit 3 towards right from its place = 4913

         Therefore, 4931 > 4913

3. In the greatest 5-digit number, if the tens and thousands digits are exchanged, then the difference between the original number and new number is

(i) 99990

(ii) 0

(iii) 1

(iv) 90000

Answer:

3. (ii) 0