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Exponents: Engineering Notation (page 4 of 5)

Sections: Basics, Negative exponents, Scientific notation, Engineering notation, Fractional exponents

"Engineering" notation is very similar to scientific notation, except that the power on ten can only be a multiple of three. In this way, numbers are always stated in terms of thousands, millions, billions, etc. For instance, 13,460,972 is thirteen million and some. In the newspaper, it would probably be abbreviated as "13.5 million". In engineering notation, you would move the decimal point six places to get 13.460972 × 10⁶. Once you get used to this notation, you recognize that 10⁶ means "millions", so you would see right away that this is around 13.5 million. Every time a newspaper refers to some number of millions or billions or trillions, rather than writing out the whole number with all the zeroes, it is, in effect, using engineering notation.

• Express 472,690,128,340 in engineering notation.

This is a twelve-digit number. You need to move the decimal point from the end of the number toward the beginning of the number, but you must move it in steps of three decimal places. In this case, you must move the decimal point to between the 2 and the 6, because this will leave nine digits (and nine is a multiple of 3) after the decimal point, and no more than three digits before the decimal point. Then the answer is:

472.690128340 × 10⁹, or 472.7 billions.

• Express 83,201 in engineering notation.

You need to move the decimal point over to the left in sets of three digits. You can't move the decimal point any further than to the left of the 2, which is three places, so the answer is:

83.201 × 10³, or 83.201 thousands.

• Express 0.000 063 8 in engineering notation.

You need to move the decimal point over in sets of three. If you move the decimal point to the right three places, you'll be left with "0.0638", which won't do. If you move the decimal point to the right nine places, you'll get "63800", which is too many digits. So move the decimal point six places. Since this started out as a small number, the power on 10 will be negative, so the answer is:   Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

63.8 × 10^–6, or 63.8 millionths.

• Express 0.397 53 in engineering notation.

Move the decimal point to the right three places. Since this started as a small number, the power on 10 will be negative:

397.53 × 10^–3, or 397.53 thousandths.

You should notice that, in engineering notation, it is perfectly okay to have more than one digit to the left of the decimal point -- in fact, you should expect to have something other than always only one digit. Just make sure that the power on 10 is a multiple of three.

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