Question

Give a rough estimate \[(\] by rounding off to nearest hundreds \[)\] and also a closer estimate \[(\] by rounding off to nearest tens \[)\] \[:\]
 \[(a)\] \[439+334+4,317\]
 \[(b)\] \[1,08,734-47,599\]
 \[(c)\] \[8,325-491\]
 \[(d)\] \[4,89,348-48,365\]

Answer 1

Hint: Firstly we have to round off the nearest hundred by taking the last three digits of the given term and then we have to round off the nearest tens by taking the last two digits of the given term. After that we have to find the sum of the obtained result to obtain the given solution.

Complete step-by-step answer:
The process of expressing a number nearest to a figure which is easier to understand is called rounding off numbers.
The round off numbers, follow this rule:
Look at the digit just to the right of the digit to be rounded.
If that digit is less than \[5\] , change all the digits to the right of the rounding digit to zero.
If that digit is greater than or equal to \[5\] , add one to the rounding digit and change all digits to the right of the rounding digit to zero.

 \[(a)\] \[439+334+4,317\]
Rough estimate:
We have to find the nearest hundreds by taking last three digits
 Rounding off \[439\] to nearest hundreds we will get \[400\]
 Rounding off \[334\] to the nearest hundreds we will get \[300\]
Rounding off \[4,317\] to the nearest hundreds we will get \[4,300\]
Now, add all the obtained results that is \[,\] \[400+300+4,300=5,000\]
Estimated Sum \[=5,000\]
Closer Estimate:
We have to find the nearest tens by taking last two digits
Rounding off \[439\] to nearest tens we will get \[440\]
Rounding off \[334\] to nearest tens we will get \[330\]
Rounding off \[4317\] to nearest tens we will get \[4320\]
Now, add all the obtained results that is \[,\] \[440+330+4,320=5,090\]
Estimated Sum \[=5,090\]

 \[(b)\] \[1,08,734-47,599\]
Rough Estimate:
We have to find the nearest hundreds by taking last three digits
Rounding off \[1,08,734\] to nearest hundreds we will get \[1,08,700\]
Rounding off \[47,599\] to nearest hundreds we will get \[47,600\]
Now subtracting the obtained result that is \[1,08,700-47,600=61,110\]
Estimated difference \[=61,110\]
Closer Estimate:
We have to find the nearest tens by taking last two digits
Rounding off \[1,08,734\] to nearest tens we will get \[1,08,730\]
Rounding off \[47,599\] to nearest tens we will get \[47,600\]
Now subtracting the obtained result that is \[1,08,730-47,600=61,130\]
Estimated difference \[=61,130\]

 \[(c)\] \[8,325-491\]
Rough Estimate:
We have to find the nearest hundreds by taking last three digits
Rounding off \[8325\] to nearest hundreds we will get \[8300\]
Rounding off \[491\] to nearest hundreds we will get \[500\]
Now subtracting the obtained result that is \[8,300-500=7,800\]
Estimated Difference \[=7,800\]
Closer Estimate:
We have to find the nearest tens by taking last two digits
Rounding off \[8325\] to nearest tens we will get \[8330\]
Rounding off \[491\] to nearest tens we will get \[490\]
Now subtracting the obtained result that is \[8,330-490=7,840\]
Estimated Difference \[=7,840\]

 \[(d)\] \[4,89,348-48,365\]
Rough Estimate:
We have to find the nearest hundreds by taking last three digits
Rounding off \[4,89,348\] to nearest hundreds we will get \[4,89,300\]
Rounding off \[48,365\] to nearest hundreds we will get \[48,400\]
Now subtracting the obtained result that is \[4,89,300-48,400=4,40,900\]
Estimated Difference \[=4,40,900\]
Closer Estimate:
We have to find the nearest tens by taking last two digits
Rounding off \[4,89,348\] to nearest tens we will get \[4,89,350\]
Rounding off \[48,365\] to nearest tens we will get \[48,370\]
Now subtracting the obtained result that is \[4,89,350-48,370=4,40,980\]
Estimated Difference \[=4,40,980\]

Note: If the number is \[0-4\] then it is known as round down, If the number is \[5-9\] then it is known as round up.But here you need to know at what situations you are doing rounding off.Like in this case counted \[97\] cows in his field , but when he rounded them up he had \[100\] cows.