Question

Give a rough estimate (by rounding off to nearest hundreds) and also a closer estimate (by rounding off to nearest tens):
$8325-491$

Answer 1

Hint: First, we will round the value 8325 to its nearest hundreds value i.e. 8300 and similarly, 491 to its nearest hundreds value i.e. 500. On taking the difference between these two numbers, we will get a closer estimated difference. Then, we will do the same for rounding off to nearest tens.

Complete step-by-step answer:
Here, we are asked to find a difference of $8325-491$ not accurate by a rough estimate.
So, here we will convert 8325 to nearer hundreds value. We can write it as 8400 and 8300 because 8325 lies between it. Now, we can see that there is more gap from 8325 to 8400 as compared to 8325 to 8300. So, we can round off 8325 to be 8300.
Similarly, 491 lies between 400 and 500. As we can see 491 is far from 400 and close to 500. So, we can also round off 491 as 500.
Now, we have an equation to be solved as $8300-500$ . On solving this we will get an estimated difference of 7800.
Thus, a rough estimate of $8325-491$ is 7800.
Similarly, we will convert 8325 to nearer tens value. We can write it as 8320 and 8330 because 8325 lies between it. Now, we can see that there is the same gap from 8325 to 8320 as well 8325 to 8330. So, we can round off 8325 to be 8330.
Similarly, 491 is very close to 490. So, we will take as 490.
Now, we have an equation to be solved as $8330-490$ . On solving this we will get a closer difference as 7840.
 Thus, a closer estimate of $8325-491$ is 7840.

Note: Here, we can do verification whether our estimated answer is closer to the actual answer or not. If we take the difference of $8325-491$ , we will get 7834 which is closer to our estimated value of 7800. Now, if we assume that 8325 to be 8400 and 491 to be 400 then, there will be more difference. Thus, we will have $8400-400=8000$ which will not be considered to be correct. Similarly, we can check for tens value also. So, we have to round off value in such a way, that there should not be much more gap between the actual answer and estimated answer.