13.5 Comparing Powers of Ten
Name: _______________________ Per _____
BIG IDEA:
It is “simpler” to write HUGE or TINY numbers using powers of ten. For example:
1,000,000,000,000,000,000,000,000,000,000 (there are 30 zeros) is the same as 1030
0.000000000000001 (there are 14 zeros) is the same as 10-15
SIMPLIFY these numbers by writing them as 1 times a power of ten, for example 1 x 109
1. One septillion: 1,000,000,000,000,000,000,000,000 =
2. One quadrillion: 1,000,000,000,000,000 =
3. One undecillion: 1,000,000,000,000,000,000,000,000,000,000,000,000 =
4. One trillion: 1,000,000,000,000 =
5. 0.00000001 =
6. 0.00001 =
7. 0.000000000000001 =
SIMPLIFY these numbers by writing them as a SCALAR times a power of ten, for example: 3 x 1011
8. 6,000,000,000,000 miles in a light year =
9. 9,000,000,000,000,000,000,000,000 =
10. one amu is about 0.0000000000000000000000000002 kilograms =
11. 0.000000000005 =
Complete the table.
Planet
12.Mercury
13.Venus
14.Earth
15.Mars
16.Jupiter
17.Neptune
18.Pluto
Average distance
Round to the
from the sun in
nearest whole
miles
“illion”
36,977,218
40,000,000
67,356,001
93,763,217
117,002,032
492,543,003
2,800,045,496
3,720,480,033
Write as a scalar
times a power of
ten
4 x 107
BIG IDEA:
RATIOS are how we make COMPARISONS in math. RATIOS are division problems.
Therefore, COMPARISONS are made by DIVIDING two things. The result is called a
SCALAR or “scale factor” (which is just a multiple). For example, it takes BillyBob 48 minutes
to complete this homework assignment. It takes BettySue 24 minutes to complete the same
assignment. 48/24 is 2. 2 is the SCALAR, or scale factor. In other words, it takes BillyBob
2 times as long to complete the assignment. Or…BettySue can complete 2 assignments in the
same time as it takes BillyBob to complete 1.
SHOW ALLWORK. Set-up the comparison and determine the scalar (or scale factor).
Write the scale factor as a power of ten AND ALSO as a standard, regular ‘ol number.
19. An average human weighs 7 x 101 kg. An average grasshopper weighs 3 x 10-4 kg. How many times
heavier is a human than a grasshopper?
20. In 2008 Apple sold about 11 million iphones (or about 1 x 107). In 2014 they sold about 169 million
iphones (or about 2 x 108). In just 6 years, Apple has increased their sales of iphones by how many times?
21. The distance from the earth to the moon is about 4 x 108 meters. The length of a fly is about 1 x 10-2.
How many flies would it take to cover the distance from the earth to the moon? (Good question, huh?)