Question

Estimate the difference of 15875 and 7892 by rounding off each number to nearest hundred
(a) 7893
(b) 8100
(c) 7900
(d) 8000

Answer 1

Hint: We solve this problem first by rounding off the given two numbers.
There are mainly two rules of rounding off the numbers.
(1) Decide the number to be rounded off and leave it same if the digit next to it less than 5
(2) Increase the digit by 1 if the digit next to it is 5 or greater than 5
By using the above rules we round off the given numbers to nearest 100 and find the difference.

Complete step by step answer:
We are given that the numbers are 15875 and 7892
Let us take the first number as
\[\Rightarrow x=15875\]
We know that the rules of rounding off as
(1) Decide the number to be rounded off and leave it same if the digit next to it less than 5
(2) Increase the digit by 1 if the digit next to it is 5 or greater than 5
By using the above rules let us round off the given number to nearest ten
Here we can see that the digit in tenth place is 7 and the digit next to it is 5
By using the second rule we get
\[\Rightarrow x=15880\]
Now, let us round off the number to the nearest hundred.
Here we can see that the digit at hundredth place is 8 and the digit next to it is 8
By using the second rule then we get
\[\Rightarrow x=15900\]
Now, let us take the second number as
\[\Rightarrow y=7892\]
Now let us round off the number to nearest tens
Here, we can see that the digit at tens place is 9 and digit next to it is 2
By using the first rule we get
\[\Rightarrow y=7890\]
Now, let us round off the number to the nearest hundred.
Here we can see that the digit at hundredth place is 8 and the digit next to it is 9
By using the second rule then we get
\[\Rightarrow y=7900\]
Now, let us assume that the difference of given numbers as \[d\] then we get
\[\begin{align}
  & \Rightarrow d=x-y \\
 & \Rightarrow d=15900-7900 \\
 & \Rightarrow d=8000 \\
\end{align}\]
Therefore we can conclude that the difference of two numbers is 8000.

So, the correct answer is “Option d”.

Note: We can solve this problem by directly rounding off the number to its hundreds place.
We have the first number
\[\Rightarrow x=15875\]
By rounding off the number to nearest hundred directly that is the number at hundredth place is 8 and next digit is 7 so, by using the second rule we get
\[\Rightarrow x=15900\]
Similarly we have the second number as
\[\Rightarrow y=7892\]
Here we have the digit in hundredth place as 8 and the next digit is 9
By using the second rule we get
\[\Rightarrow y=7900\]
Now, let us assume that the difference of given numbers as \[d\] then we get
\[\begin{align}
  & \Rightarrow d=x-y \\
 & \Rightarrow d=15900-7900 \\
 & \Rightarrow d=8000 \\
\end{align}\]
Therefore we can conclude that the difference of given two numbers is 8000.
So, option (d) is the correct answer.