Estimation Or Approximation

 

Estimation, or approximation, is a method using which we arrive at the nearest answer, say to the nearest 10 or 100, if we are working with bigger numbers. Probably the simplest way to estimate is to round all the numbers that we are working with to the nearest 10, 100 or 1000 and then do the necessary sum.

Rounding

Rounding is one simplest way of estimation. This is where you make a long number simpler by ‘rounding’, or expressing in terms of the nearest unit, ten, hundred, tenth, or a certain number of decimal places.

For example, 1,764 to the nearest thousand is 2,000. To the nearest 100 it is 1,700. To the nearest ten it is 1,750.   You need to simply look at the number on the right of the level that you are rounding to and see whether it is closer to 0 or 10.

Demonstration:

Express 166 to the nearest 10,  As you are rounding to the nearest 10 you know that you need at least 100, and then to work out whether the nearest 10 is 60 or 70, you look at the units. 6 is more than five, so you round up. The answer is 170.

(I) Estimate the sum by rounding each number to the nearest hundred and then adding

      728 + 711.   The sum is approximately (700+700) = 1400

(II) Estimate the sum by rounding each number to the nearest thousand and then adding

       9,325 + 9,286. The sum is approximately(9000+9000) = 18000.

(III) Estimate the difference by rounding each number to the nearest hundred and then

        Subtracting 877 – 633. The difference is approximately (800 – 600) = 200.

(IV)  Estimate the product. Round each factor to the nearest ten, then multiply 78 × 94.

       The product is  approximately (80 X90) = 7200.

(V) A house painter has Rs.381 to buy paint. If each can of paint costs Rs.2, about how many

       cans of paint can the painter buy? Choose the better estimate, 220 or 190.

       Answer: 190.

If we Divide 381 by 2 we get 190.5 , this is nearest to 190.