Estimation in Operations on Numbers

To estimate sum and difference, we first round off each number to the nearest tens, hundreds, thousands or millions and then apply the required mathematical operation.

Solved example on Estimation in Operations on Numbers:

1. Find the actual and estimated sum of 126,289 and 375,484 by rounding off numbers to the nearest thousands.

Solution:

To round off to the nearest thousands place, we consider the number at ten-thousands place. Let us see the position of 126,289 on the number line.

$Round off to the Nearest Thousands Place$

We observe that 126,289 is closer to 100,000. Therefore, it is rounded down to 100,000. Next, we check the position of 375,484 on the number line.

$Estimation in Operations on Numbers$

We note that 375,484 is closer to 400,000. Therefore, it is rounded up to 400,000.

$Actual Sum Vs. Estimated Sum$

To find the estimated product or quotient, we round off numbers to the greatest place-value.

2. Find the actual and estimated product of 22,165 and 3,745 by rounding off numbers to the greatest place-value.

Solution:

22,165 is rounded off to the nearest ten-thousands. 3745 is rounded off to the nearest thousands.

$Actual Product Vs. Estimated Product$

3. Estimate the quotient for 7,475 ÷ 510

Solution:

7,475 is rounded off to the nearest thousands

510 is rounded off to the nearest hundreds

7,475 is closer to 7,000

510 is closer to 500

$Estimate the Quotient$

So, 7,000 ÷ 500 = 14

Questions and Answers on Estimation in Operations on Numbers:

I. Estimate the given numbers and find the answer:

$Estimate the given Numbers$

Answer:

$Estimate the given Numbers Answer$

II. Estimate and choose the right answer:

1. A shopkeeper has 93,450 packets to sketch pens. If each packet has 12 pens, then how many sketch pens are there in the shop.

(i) 900,000

(ii) 9,540,000

Answer: 900,000

2. Shelly has 6,782,344 mm of rope. She has another rope of length 2,539,886 mm. If both the ropes are attached, the estimated length nearest to 1000 will be

(i) 9,450,000

(ii) 9,322,000

Answer: 9,322,000

3. There are 1341 houses in a street. Each house uses 278 units of electricity energy. Estimated energy used by the houses nearest to 10 will be

(i) 375,200

(ii) 37,500

Answer: 375,200

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