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Scientific Notation and Metric Prefixes
5 questions By Tony R. Kuphaldt
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Question 4 of 5
Metric prefixes are nothing more than “shorthand” representations for certain powers of ten. Express the following quantities of mass (in units of grams) using metric prefixes rather than scientific notation, and complete the “index” of metric prefixes shown below:
8.3 ×1018 g = 3.91 ×1015 g = 5.2 ×1012 g = 9.3 ×109 g = 6.7 ×106 g = 6.8 ×103 g = 4.5 ×102 g = 8.11 ×101 g = 2.1 ×10−1 g = 1.9 ×10−2 g = 9.32 ×10−3 g = 1.58 ×10−6 g = 8.80 ×10−9 g = 6.9 ×10−12 g = 7.2 ×10−15 g = 4.1 ×10−18 g = 
Reveal answer8.3 ×1018 g = 8.3 Eg 3.91 ×1015 g = 3.91 Pg 5.2 ×1012 g = 5.2 Tg 9.3 ×109 g = 9.3 Gg 6.7 ×106 g = 6.7 Mg 6.8 ×103 g = 6.8 kg 4.5 ×102 g = 4.5 hg 8.11 ×101 g = 8.11 dag 2.1 ×10−1 g = 2.1 dg 1.9 ×10−2 g = 1.9 cg 9.32 ×10−3 g = 9.32 mg 1.58 ×10−6 g = 1.58 μg 8.80 ×10−9 g = 8.80 ng 6.9 ×10−12 g = 6.9 pg 7.2 ×10−15 g = 7.2 fg 4.1 ×10−18 g = 4.1 ag 
Notes:Once students realize metric prefixes are nothing more than shorthand for certain powers of ten, they see that scientific and metric notations are really one and the same. The only difficult part of this is committing to memory all the different metric prefixes and their respective powers of ten. Be sure to mention that the power of ten that are multiples of three (103, 106, 10−12, etc.) are more commonly used than the other powers (h, da, d, and c).
In case anyone asks, the metric prefix for 101 (deka) is sometimes spelled deca. There seems to be no “standard” way to spell the name of this prefix.
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Question 5 of 5
What is the difference between the following three values of mass (in kilograms)?
4 ×102 kg 4.5 ×102 kg 4.500 ×102 kg Reveal answerThe difference between these figures is precision: the degree of uncertainty in the value expressed.
Notes:It is important for students to understand that although a computer may see these three quantities as precisely equivalent, they are actually not. Human beings do not write extra zeros if they do not have to, and so these zeros serve to indicate extra certainty in the figure.
