Question

Round off to nearest thousands. The given number is \[76,823\].
\[A)\] \[76,000\]
\[B)\] \[75,000\]
\[C)\] \[77,000\]
\[D)\] \[78,000\]

Answer 1

Hint: Here we will either round up or round down the number to its nearest thousands as per the face value of the digit in the hundreds place. On doing some simplification we get the required answer.

Formula used: Suppose a number is in the form of thousands.
Let say, the number is \[A,BCD\], where \[A,B,C,D\] are different or same single digits
So, if we want to make this number to its nearest thousands, then we will follow the following rules:
\[i)\] If the digit in the hundred’s place is greater than or equal to \[5\], then we will add \[1\] to the digit in the thousand’s place, and we will put \[0\] in hundreds place, ten’s place and one’s place and face value of the rest of the places will remain same.
So, the digit in hundreds place will be \[ = (A + 1).\]
And, other digits will become zero, \[B = C = D = 0.\]
\[ii)\] If the digit in the hundred’s place is lesser than \[5\], then we will put the same digit in hundreds place as it was in original number, and we will put \[0\] in hundreds place, ten’s place and one’s place and face value of the rest of the places will remain same.
So, the digit in hundreds places will be \[ = A\].
And, other digits will become zero, \[B = C = D = 0.\]

Complete step-by-step solution:
The given number is \[76,823\].
Now, the digit in hundreds places is \[8\], which is greater than \[5\].
So, as per the above rules:
We have to add \[1\] to the digit in thousand’s place, and we will put zero to the hundreds place, ten’s place, one’s place and the digits will stay the same in all other places.
So, the digit in thousand’s place will become \[ = 6 + 1 = 7.\]
So, after rounding off, the required nearest thousands of \[76,823\] will become \[77,000\].

\[77,000\] is the correct answer.

Option C is the correct answer.

Note: An alternate process can be used to solve this kind of problem.
We can draw this number in a line graph and then we can check whether the number is closest to the latter half or the earlier half.
So, we will draw a range of \[76,000 - 77,000\] in a line graph.

So, if we look at it closely, we can say that \[76,823\] is very much closer to the \[77,000\].
So, rounding off to the nearest thousands means finding the number which is nearest to multiple of its thousand’s place.
So, we can say that \[77,000\] is the nearest thousands of \[76,823\], when we round it off to its nearest thousands.