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Number Notations, Arithmetical Operations, and Calculators
PROBLEM:
We are told that the population of a city is 256,700 and that the assessed value of
the property is $653,891,600. Find an approximate value of the assessed property
per capita.
SOLUTION:
We need to evaluate the division
$653,891,600 9
256,700 ~ '
First we write the numbers in standard scientific notation:
6.538916 x 10
8
2.56700 x 10
5
Round off to
6.5 x 10
8
2.6 x 10
5
Mental arithmetic gives
10
8
— = 10
3
10
5
The approximate answer is $2.5 x 10
3
, or $2500. This happens to be a very close
estimate; the value obtained with a calculator is $2547.30.
PROBLEM:
Find an approximate value for
2783 x 0.00894 x 0.00532
1238 x 6342 x 9.57
SOLUTION:
First rewrite in scientific notation but, instead of using standard form, set the
decimal points to make each lefthand factor as near to 1 as possible:
2.783 x IP
3 x 0.894 x 10~
2 x 5.32 x 10~
3
1.238 x 10
3 x 6.342 x 10
3 x 0.957 x 10
1
Rewrite the lefthand factors rounding off to integers:
3 x IP
3 x 1 x 1Q2 x 5 x 10~
3
1 x 10
3 x 6 x 10
3 x 1 x 10'
Multiplication now gives