Estimation Of Numbers

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Unit: Number System

Chapter: Estimation of Numbers

Reference: – Introduction to Estimation, Rounding Off Numbers (Nearest Tens, Hundreds, Thousands), Estimating Sums and Differences, Estimating Products and Quotients, Front-End Estimation, General Rule for Estimation, Real-Life Applications

After studying this chapter, you should be able to understand:

• Introduction to Estimation & Its Need
• Rounding Off Numbers to Nearest Tens, Hundreds, Thousands
• Estimating Sums, Differences, Products & Quotients
• Front-End Estimation
• Application of Estimation in Real Life

Estimation of Number

 

Estimation is a quick approximation of numbers close to actual solution when it is difficult to determine the exact number. Estimation can help us in various ways-

• It can save us time and help us plan. For example, according to the speed of the car, we can estimate approximately how much time would be required by us to reach a place.
• It can save us money if we quickly estimate how much to pay. Suppose we go to buy 15 chocolates and the shopkeeper tells us that 1 chocolate costs $0.31 and asks us to pay $6.05.  We can quickly estimate that 20 chocolates would cost us around $6.00 and so we can correct the shopkeeper that the shopkeeper might have made some mistake in the calculation of the total cost.
• It helps us to ensure correct calculations.

 

We can estimate numbers by -

• Rounding off Numbers
• Estimating outcomes of number situations

 

 

Rounding off a number to nearest tens -

When we round off the units place it is called estimating a number to nearest tens.

• If the number at units place is below 5, it is rounded off to 0 i.e. the lower tens.
• If the number at units place is greater than or equal to 5, it is rounded off to 10.

Examples
        (i) 88 is rounded off to the nearest ten as 90

        (ii) 34 is rounded off  to the nearest ten as 30

        (iii) 12 is rounded off  to the nearest ten as 10

 

 

Rounding off a number to nearest hundreds -

When we round off the tens place it is called estimating a number to nearest hundreds.

• If the number at tens place is below 5, it is rounded off to 0.
• If the number at tens place is greater than or equal to 5, it is rounded off to 100.

 

Examples
        (i) 321 is rounded off to the nearest hundred as 300

        (ii) 579 is rounded off to the nearest hundred as 600

        (iii) 452 is rounded off to the nearest hundred as 500

 

 

Rounding off a number to nearest thousands -

When we round off the hundreds place it is called estimating a number to nearest thousands.

• If the number at hundreds place is below 5, it is rounded off to 0.
• If the number at hundreds place is greater than or equal to 5, it is rounded off to 100.

 

Examples
        (i) 3951 is rounded off to the nearest hundred as 4000

        (ii) 1346 is rounded off to the nearest hundred as 1000

        (iii) 8569 is rounded off to the nearest hundred as 9000

 

Estimation of Sum or Difference -

When we estimate sum or difference, we should know why we are rounding off to have an idea of the place to which the rounding is needed.
 

Examples-

(i)      Matt has $48.88 in cash and  $90.75 in his saving account. Matt would like to buy a microwave oven worth $120. Will he have sufficient money to buy?

When we round off numbers to the nearest tens-

48.88 is rounded off to 50

90.75 is rounded off to 90

Estimated Sum = 50 + 90 = $140

We see that the Matt would have $140 approximately. So, he would have sufficient money to buy a microwave oven.

 

(ii)      Estimate 3686 + 17376

When we round off numbers to the nearest thousands-

17376 is rounded off to 17000

3686 is rounded off to 4000

So, the estimated sum is:

17000 + 4000 = 21000

(iii)     Estimate 1248 – 681

When we round off these numbers to the nearest hundreds-

1248  is rounded off to 1200

681 is rounded off to 700

So, the estimated difference is:

1200 – 700 = 500

 

 

Estimation of the Product -

To estimate the product, round off each factor to its greatest place, then multiply the rounded off factors.

 

Example-

Estimate 72 × 497.

Now, the first number 72, can be rounded off to the nearest ten as 70.

The second number 497, can be rounded off to the nearest hundred as 500.

So, the estimated product =70 × 500 = 35,000.

 

# Estimating the outcome of number operations is useful in checking the calculations.