Ch1 Scientific Notation (Powers of Ten)
1. From Table 1-3 (p.7), fill in the following blanks
109 = ____________________
10-6 = 0.000 001
_________ = 1,000
100 = ____________________
_________ = 0.01
103 = ____________________
________ = 0.001
2. In the “powers-of-ten” notation, the superscript is called an ____________ and is
equal to _________________________________________________________.
The exponent is also equal to ________________________________________.
(p.9, 2nd paragraph)
3. In “powers-of-ten” notation, what does negative exponent stand for? Give an
example. (p.9, 3rd paragraph)
4. The following steps can help you express a number in “powers-of-ten” notation:
a) Identify the decimal point in the number.
b) Move the decimal point to the left (or right) until there’s only one non-zero digit
in front of the decimal point. This is the “number in front”
c) Count how many times the decimal point is moved in step (b), this is the
“exponent”. It is positive if the decimal point is moved to the left in step (b);
negative if the decimal point is moved to the right in step (b).
e) The number expressed in “powers-of-ten” notation should be:
Number in front x 10exponent
For example,
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The radius of visible universe = 40,000,000,000,000,000,000,000,000 m, to
express this number in powers-of-ten notation, we first locate the decimal point:
140,000,000,000,000,000,000,000,000
.
Decimal point
Then we move the decimal point to the left 26 times till there is only one non-zero
digit in front of decimal point, hence the “number in front” = 1.4. Since the
decimal point is moved to the left, the exponent should be positive, so the
exponent = 26. The number, expressed in powers-of-ten notation, is:
1.4 x 1026 m
Another example,
The radius of a proton = 0.000 000 000 000 001 2 m. To write this number in
powers-of-ten notation, we first identify the decimal point:
.
0 000 000 000 000 001 2
Decimal point
Then we move the decimal point to the right 15 times till there’s only one nonzero digit in front of the decimal, hence the “number in front” = 1.2. Since the
decimal point is moved to the right, the exponent is negative, so the exponent =
-15. The number, expressed in powers-of-ten notation, is:
1.2 x 10-15 m
5. Exercise 5 (pg.12) (Don’t forget to include unit in your final answer)
6. Exercise 6 (pg.12)
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7. To write a power-of-ten number as ordinary number,
a) If the exponent is positive, we multiply the “number in front” by 10 the number
of times of the exponent. For example, 4.3 x 103 g equals 4.3 multiplied by 10
three times:
4.3 x 103 g = 4.3 x 10 x 10 x 10 g = 4.3 x 1000 g = 4300 g
b) If the exponent is negative, we divide the “number in front” by 10 the number
of times of the exponent. For example, 8.12 x 10-5 m equals 8.12 divided by 10
five times:
8.12 x 10-5 m = 8.12 /100000 m = 0.0000812 m
8. End of Chapter Exercise 8 (pg.13)
9. What are the rules for multiplication and division of powers of ten? (pg.10-11,
“Powers of Tens” Computing box)
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10. Exercise 9 (pg.13) with your steps shown as in Computing box on p.11.
11. Exercise 10 (pg.13) with your steps shown as in Computing box on p.11.
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