Question

Round off 1289 to the nearest 10, 100 and 1000.

Answer 1

Hint: Use the rules of rounding off a number to find the numbers which are the rounded-off values of 1289 to the nearest 10s, 100s or 1000s place.

Complete step-by-step solution -

Rounding off a number:
We select the precision first, i.e. up to which decimal place should we round off.
All the values after that decimal place are dropped, i.e. they are occupied by the digit 0.
If the value at that decimal place is greater than or equal to 5, then we increase the value of the digit before that decimal place by 1 and the digit at that decimal place is changed to 0.
If the value at that decimal place is less than 5, then we change the digit at that decimal place to 0.
Suppose we want to convert 1254 to the nearest 10s place.
So rounding off place = one's place.
All the digits after one's place are changed to 0.
So we are left with 1254
Now since the digit at one's place = 4 is less than 5, we keep all the digits before one's place the same and change the digit at one's place to 0.
Hence the rounded off value of 1254 to the nearest 10 is 1250.

Rounding off 1289 to the nearest 10:
Rounding off place = one's place
The digit at one's place = 9, which is greater than 5.
Hence we increase the digit at 10s place by 1, 8+1 = 9.
We change the digit at one's place to 0.
Hence the rounded off value of 1289 to the nearest 10 is 1280.
Rounding off 1289 to the nearest 100s place:
Rounding off place = Tens place
Hence the digit at one's place is changed to 0.
We have a new number as 1280.
The digit at tens place is 8, which is greater than 5.
Hence we increase the digit at 100s place by 1 and change the digit at 10s place to 0.
Hence the rounded off value of 1289 to the nearest 100s place is 1300.
Rounding off to the nearest 1000s place:
Rounding off place = 100s place.
Hence the digits at one's place and 10s place are changed to 0.
Hence the new number is 1200.
Now the digit at 100s place is 2, which is less than 5.
Hence the rounded off value of 1289 to the nearest 1000s place is 1000.

Note: Note that if the digit whose value is increased by 1 is 9, then carry the 1 to the next decimal place like in addition.
Eg. We want to round off 1299 to the nearest 10s place.
Since the digit at units place is 9 which is greater than 5, we increase the digit at tens place by 1.
Now 9+1 = 10
The one is taken as carry and added to 2.
So we get rounded off value as 1300.
Note that the answer 12100 will be incorrect.
Also, note that the round off error cannot be more than the place value of the decimal place nearest to which is the rounding done, i.e. if a number is rounded off to nearest 10, then the round of error cannot be more than 10. This can be done to verify whether the rounding off was correctly done or not.