SCIENTIFIC NOTATION
Review of Introductory Mathematics
Using the results of the previous chapter, the following whole numbers and decimals can be
expressed as powers of 10:
1 =100
0.1 = 1/10 = 10-1
10 =101
0.01 = 1/100 = 10-2
100 =102
0.001 = 1/1000 = 10-3
1000 =103
10,000 =104
A number N is in scientific notation when it is expressed as the product of a decimal number
between 1 and 10 and some integer power of 10.
N = a x 10n where 1 < a < 10 and n is an integer.
The steps for converting to scientific notation are as follows:
Step 1:
Place the decimal immediately to the right of the left-most non-zero
number.
Step 2:
Count the number of digits between the old and new decimal point.
Step 3:
If the decimal is shifted to the left, the exponent is positive. If the decimal
is shifted to the right, the exponent is negative.
Let us examine the logic of this. Consider as an example the number 3750. The number will
not be changed if it is multiplied by 1000 and divided by 1000 (the net effect is to multiply it
by one). Then,
3750
1000
× 1000
3.750 × 1000
3.750 × 103
There is a division by 10 for each space the decimal point is moved to the left, which is
compensated for by multiplying by 10. Similarly, for a number such as .0037, we multiply the
number by 10 for each space the decimal point is moved to the right. Thus, the number must
be divided by 10 for each space.
MA-01
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