Question

Ram estimated the sum of $120$ and $240$ rounded off to hundreds in two ways.

Method 1: He approximated the individual values correct to hundreds place and then added the numbers.

Method 2: He added the numbers and then approximated the sum correct to hundreds place.

Find the difference between the answers obtained by the two methods.

Answer 1

Step 1: Approximate the individual values

If the digit to the right of rounding place is $0,1,2,3,4$ ,we do not change the digit on rounding off place but change change all the digits to the right of it to zero and if the digit to the right of rounding off place is $5,6,7,8,9$ ,we add $1$to the digit on the rounding off place and change all the digits to to its right to zero.

Estimation of $120$ to hundred place, we get$=100$

Estimation of $240$ to hundred place, we get$=200$

Estimation of individual values correct to hundreds place and then adding the numbers, we get$=100+200=300$

Step 2: Approximate the sum

Adding $120$ and $240$, we get$=120+240=360$

Rounding off $360$ to hundred place, we get $400$.

Step 3: Find the difference

Difference of $400$ and $300$, we get$=400-300=100$

Hence, difference between the answers obtained by the two methods is $100$.