Download APPENDIX II "Manipulating Numbers in Scientific Notation" Answers

APPENDIX II
"Manipulating Numbers in Scientific Notation" Answers
Practice:
1. Write the following numbers in scientific notation; keep only 3 significant figures.
a)
b)
c)
d)
e)
9,876,543
1,000
1,000,000,000
0.000009876543
0.000000001000
9.88 x 106
1.00 x 103
1.00 x 109
9.88 x 10–6
1.00 x 10–9
2. Multiply and divide the following numbers.
a) 108 times 10-3
108+(–3) = 105
b) 108 divided by 10-3
108–(–3) = 1011
c) 14 x 1015 times 2 x 10-12
(14 x 2) x 1015+(–12) = 28 x 103 = 2.8 x 104
d) 14 x 1015 divided by 2 x 10-12
(14 ൊ 2) x 1015–(–12) = 7 x 1027
e) (9 x 109)(1.6 x 10-19)(1.6 x 10-19) divided by (5 x 10-5)
(9 x 1.6 x 1.6 ൊ 5) x 109+(–19)+(–19)–(–5) = 4.608 x 10–24
Ciardi, T Scientific Notation 1 3. A wavelength of blue light is 450 nanometers or 450 x 10–9 meters. What is this wavelength in
standard notation?
450 x 10–9
Since this is a negative exponent, we need to move the decimal to the left, nine places.
450 x 10–9 = 0.000000450
4. Our sister galaxy, the Andromeda galaxy is 250 Million light years, or 250 x 106 light years
from us, and 1 light year is 9.46 x 1015 meters. If we multiply the two numbers together, the
number of light years times the number of meters in a light year, we can know the total distance
in meters. Write the total distance in meters to the Andromeda Galaxy, in standard notation.
First, multiply the numbers
(250 x 106 LY) x (9.46 x 1015 meters/LY) = 2.3 x 1024 meters
Now we can write the answer in standard notation. Since this is a positive exponent, we
need to move the decimal to the right, 24 places.
2,300,000,000,000,000,000,000,000 meters (This is why we use scientific notation)
This is 1,469,900,000,000,000,000,000 miles!
Ciardi, T Scientific Notation 2