SCIENTIFIC NOTATION Review of Introductory MathematicsUsing the results of the previous chapter, the following whole numbers and decimals can beexpressed as powers of 10:1 =10^{0}0.1 = 1/10 = 10^{-1}10 =10^{1}0.01 = 1/100 = 10^{-2}100 =10^{2}0.001 = 1/1000 = 10^{-3}1000 =10^{3}10,000 =10^{4}A number N is in scientific notation when it is expressed as the product of a decimal numberbetween 1 and 10 and some integer power of 10.N = a x 10^{n}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-zeronumber.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 decimalis shifted to the right, the exponent is negative.Let us examine the logic of this. Consider as an example the number 3750. The number willnot be changed if it is multiplied by 1000 and divided by 1000 (the net effect is to multiply itby one). Then,37501000× 10003.750 × 10003.750 × 10^{3}There is a division by 10 for each space the decimal point is moved to the left, which iscompensated for by multiplying by 10. Similarly, for a number such as .0037, we multiply thenumber by 10 for each space the decimal point is moved to the right. Thus, the number mustbe divided by 10 for each space.MA-01 Page 68 Rev. 0

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