Estimating the Results of Operations-I

Sam and Roy are friends.

They wanted to find the amount they saved for past two months in the bank

Sam saved 896 and 745 where as Roy saved 684 and 965.

In order to know the total savings Sam started to add the numbers, But Roy came up with an estimated value of 1700 rupees

Sam asked Roy on how could he get an estimated value so easily and quickly.

Roy explained that 684 when rounded to hundreds place, gives the value as 700

Similarly 965 when rounded to hundreds place gives the value as 1000

Adding the two values Roy was able to say that it is 1700 easily which is very close to the actual value ( 684+965=1649)

Learning this Sam also esimated his total as 1700

Estimation of a Number

A number can be estimated to nearest 10, 100, 1000 and so on

Estimation of a number to tens is nothing but rounding off a number to nearest multiples of 10.

For example consider 17, 17 lies between 10 and 20 but is closer to 20 so is estimated as 20

Estimation of a number to hundreds rounding off a number to nearest multiples of 100.

For instance, 410 lies between 400 and 500 but is closer to 400 and estimated as 400

Estimation of a number to thousands is rounding off a number to nearest multiples of 1000.

Estimating 2673 to nearest thousands is as shown

Now, let's estimate the result of addition and subtraction of numbers.

Estimating the Results of Addition of numbers

First find the sum of the two numbers.

The sum of the two numbers is as shown,

Now let us find the estimate of the sum by rounding off the two numbers to nearest thousands

17986 is rounded off to 18000 and 5270 is rounded to 5000

And sum of the estimated numbers is as shown,

Estimating the Results of Subtraction of numbers

First find the difference of the two numbers

The actual difference of two number is as shown,

Now let us find the estimate of the difference by rounding off the two numbers

The greatest place in 5673 is thousands place and in 436 the greatest place is hundreds place.

Estimating 5673 to nearest thousands, we get 6000

Estimating 436 to nearest hundreds, we get 400

Therefore estimated difference is 5600

Clearly, estimated difference(5600) is not closer to the actual difference(5237). So, it is not a reasonable estimate.

Reasonable estimate can be found when both the numbers are estimated to nearest hundreds

5673 rounds off as 5700 and 436 rounds off to 400 when rounded off to nearest hundreds

Therefore estimated difference = 5700 – 400 = 5300

Clearly, estimated difference(5300) is closer to the actual difference(5237). So, it is a reasonable estimate.

Revision

Results of addition and subtraction can be estimated by rounding of the numbers we are adding or subtracting, her showthe two examples in the image

The End