MAKING ESTIMATION EASIER

Example:
Anne was supposed to estimate the product of two big numbers. She had to find the rough product of 6123 and 403. John saw her working on those numbers and decided to help her. He told her that the estimate was 2,400,000. Anne was amazed and said, "How did you do that?". John explained to her that he had used exponents to estimate the calculation. He also told her that the use of exponents makes estimation easier.


The use of exponents makes it relatively easy to multiply and divide large numbers.

Example:

If a large number such as 9000 × 600 is to be multiplied, one can merely multiply the 9 by the 6 and the factors of ten from both the multiplier and multiplicand.

9000 × 600 = 5,400,000

In exponential form :
9000 can be written as 9 × 103 to make it look simpler and for easy calculation purposes.
600 can also be written as 6 × 102

(9 × 103) × (6 × 102)

=(9 × 6) × (103 × 102)

= 54 × 105
Not only does it sound easy, but also gives a broader perspective of place value as well as added insight with respect to multiplication and division.

The same logic also holds for numbers that do not have trailing zeroes.


Example:


33457 × 4129 = 138,143,953


In exponential form :
(3 × 104) × (4 × 103)

=(3 × 4) × (104 × 103)

= 12 × 107

=120,000,000.

As compared to the size of numbers, the results are pretty close. Remember, it is only an estimation, not the exact result. Very easy, right!!!


The logic for division of numbers is pretty much the same. However, division is the inverse of multiplication. The exponents are subtracted rather than added.


Example :

104 / 102 =102.

104 - 102 = 104 - 2 = 102.


Example:
64 / 32 = 26 / 25 = 26 - 5= 21= 2