Question

A number, when rounded off to the nearest ten thousand, has a rounded off value of 30,000. What could be the five possible values of digits at the thousand and ten thousand place?

Answer 1

Hint:
Here, we will use the rules of rounding up and rounding down to find all the possible cases and the digits which can be taken by the thousands and ten thousands places in order to round off to 30,000. Hence, using these rules, we will be able to find the required five possible values of digits at the thousand and ten thousand places.

Complete step by step solution:
According to the question, a number, when rounded off to the nearest ten thousand, has a rounded off value of 30,000.
We know that rounding off numbers means adjusting the digits either up or down in order to make rough calculations easier. The result will be an estimated answer than the precise one.
Now, while rounding off the numbers to the nearest ten thousand, we should keep in mind the following facts:
If the digit in the thousand’s place is a number 0, 1,2, 3 or 4 then we have to round off that number to the nearest multiple of ten thousand which is smaller than the given number.
If the digit in the thousand’s place is a number greater than equal to 5, i.e. 5, 6, 7, 8 or 9 then we have to round off that number to the nearest multiple of ten thousand which is greater than the given number.
Therefore, in order to round off any number to its nearest ten thousand, we are required to look at the digit present in the thousand’s place.
In this question, the number has been rounded off to 30,000
Therefore, the five possible values of digits at the thousand and ten thousand place can be:

For the thousands place:
If the digits present are 1, 2, 3 or 4, then that number will be rounded off to 30,000
For example: 31000, 32134, 33845, 34291, and so on.

For the ten-thousands place:
If the digit at the ten thousand’s place is 2 and the digits at the thousands place are greater than equal to 5, i.e. 5, 6, 7, 8 or 9, then, those numbers will be rounded off to 30,000
For example: 25000, 26393, 27930, 28054, 29444, and so on.
Therefore, the four possible values of digits at the thousand’s place can be 1, 2, 3 or 4 when the ten thousands place remains the same i.e. 3 and one possible value of digit at the ten thousand’s place can be 2 when the digits at the thousands place are greater than equal to 5.
Therefore, the required five possible values of digits at the thousand and ten thousand places can be 1, 2, 3, 4 (when 3 is present in the ten thousands place) and 2 on the ten-thousand’s place respectively.

Note:
While rounding off large numbers such as a number to the nearest ten thousand, the digits in the thousands place are considered. And, if the digits are greater than equal to 5, then, that number is rounded up whereas, if the digits at the thousands place are less than 5, then, that number is rounded down. Here, round ‘up’ means to round off to the next higher number, whereas round ‘down means to round off the given number to the next lower number.