Name _____________________________
Date _______________ Pd _____
Multiplying and Dividing Numbers in Scientific Notation
I can multiply and divide with numbers expressed in scientific notation and decimal
notation.
1. Light travels at a speed of 1.86 x 105 miles per second. If a light year is the distance that light travels
in one year, how many miles are in a light year?
2. Assume that there are 20,000 runners in the New York City marathon. Each runner runs a distance
of 36 miles. IF you add together the total number of miles for all runners, how many times around
the globe would the marathon runners have gone? Let the circumference of the Earth be 2.5 x 104
miles. Calculate your answer using scientific notation.
3. Perform the following operations and express your answer in scientific notation.
a) (4.3 x 108) x (2.0 x 106)
c)
b)
(7.8 𝑥 103 )
(6.48 𝑥 105 )
(2.4 𝑥 104 )(1.8 𝑥 10−2 )
(1.2 𝑥 104 )
4. The sun produces 3.9 x 1033 ergs per second of radiant energy. How much energy does it produce in
one year (3.1 x 107 seconds)?
5. One gram of matter converted into energy yields 3.0 x 1020 ergs of energy. How many tons of
matter in the sun is annihilated every second to produce its luminosity of 3.9 x 1033 ergs per second?
(One metric ton = 106 grams)
6. The approximate volume of the visible universe (a sphere with a radius of about 14 billion light
years) is 1.1 x 1031 cubic light-years. If a light-year equals 9.2 x 1017 centimeters, how many cubic
centimeters does the visible universe occupy?
7. The NASA data archive at the Goddard Space Flight Center contains 25 terabytes of data from over
1000 science missions and investigations. (1 terabyte = 1015 bytes). How many CD-roms does this
equal if the capacity of a CD-rom is about 6 x 108 bytes?
REVIEW:
Simplify:
4𝑛4
8.
9.
3𝑛2
𝑐 9 𝑝3
𝑐 6 𝑝3
3
10. √27, and state if rational or irrational.
Solve:
11. 𝑎 + 1 = 26
2
Answer key:
1. 5.865696 x 1012 meters in one year
2. 20.8 times around the globe
3. a) 8.6 x 1014
b) 6.5 x 10-1
c) 1.5 x 103
4. 1.2 x 1041 ergs
5. 1.3 x 105 metric tons of mass
6. 8.69 x 1084 cubic centimeters
7. 4.2 x 107 CD-roms
4𝑛2
8. 3
9. 𝑐 3 𝑝0 = 𝑐 3
10. -3, rational
11. ±5