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algebra-estimate

by john
(florida)











































what is the estimation for 8,496-3,846

CHANGE the EXACT VALUES INTO APPROXIMATE NUMBERS to make numbers easier to use, and then subtract the approximate numbers.




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Jan 18, 2011
Algebra - Estimate
by: Staff

The question:

by John
(Florida)


What is the estimation for 8,496-3,846?



The answer:

This is an important question because estimating is used in every area of life (not just in math).

Estimating a number will involve ROUNDING the number - CHANGING an EXACT VALUE INTO an APPROXIMATE NUMBER.

We use approximate numbers to make numbers easier to use. For example, when someone states their age they generally state their age at their last birthday - this is generally an estimate, since they may be several months older then their last birthday.

However, ESTIMATING introduces an ERROR. While numbers which have been rounded make them easier to use, changing an exact number into an approximate number creates a problem.

Estimating a subtraction will involve ROUNDING BOTH of the NUMBERS involved BEFORE completing THE SUBTRACTION. TWO ERRORS are introduced in this process.

The point and the question is this: what degree of accuracy do you require? (or, how large an error can you tolerate?)


As you already know, the exact answer to the subtraction is:

8,496 - 3,846 = 4,650

8,496 - no error introduced since this is an exact number
3,846 - no error introduced since this is an exact number



If you round your numbers to the nearest 10 before you subtract, your estimate becomes:

8,500 - 3,850 = 4,650

8,496 - error introduced of +4 since 8,500 is greater than 8,496
3,846 ? error introduced of +4 since 3,850 is greater than 3,846

These two errors cancel one another when the numbers are subtracted



If you round your numbers to the nearest 100, you estimate becomes:

8,500 - 3,800 = 4,700


8,500 - error introduced of +4 since 8,500 is greater than 8,496
3,800 - error introduced of -46 since 3,800 is smaller than 3,846

These two errors do not errors cancel one. Together, they create an even larger error (+50) when the numbers are subtracted.



If you round your numbers to the nearest 1000, your estimate becomes:

8,000 - 4,000 = 4,000

8,000 - error introduced of -496 since 8,000 is smaller than 8,496
4,000 - error introduced of +154 since 4,000 is greater than 3,846

These two errors do not errors cancel one. Together, they create an even larger error (-650) when the numbers are subtracted.


In conclusion, you must answer the question posed earlier: how accurate do you require your estimate to be? (In exchange for using an estimate to make the numbers easier to subtract, how large an error can you tolerate?)


Thanks for writing.


Staff
www.solving-math-problems.com



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