Download Worksheet - Powers of Ten Name Date ______ Per ___ Grp ___

Worksheet - Powers of Ten
Large and
small
Name ___________________
Date _______ Per ___ Grp ___
numbers and Gravitation
Part 1 Powers of Ten
a) Positive powers - complete the tables
2
=
10 x
=
100
104
=
10 x
=
10,000
106
=
=
1,000
=
=
10
=
b) Negative powers - complete the tables
=
1
10
=
10-3
=
1 x 1 x 1
10 10 10
=
0.001
10-5
=
1 x 1 x
10 10
=
0.00001
10
10-1
0.0001 =
0.01
1 x 1 x 1
10 10 10
x
=
=
=
=
100
Special
=
Part 2 Writing Numbers in Power-of-Ten Notation
a) Positive powers - Large numbers
Calculators cannot handle huge numbers without changing the format
mass of Earth
=
6,000,000,000,000,000,000,000,000 kg
mass of Jupiter
= 1900,000,000,000,000,000,000,000,000 kg
b) Negative powers - Small numbers
0.0002 =
2 x
1 x 1 x 1 x 1
10 10 10 10
0.000 000 5
=
= 6.0 x
= 1.9 x
= 2 x 10-4
5 x 1 x 1 x 1 x 1 x 1 x 1 x 1
10 10 10 10 10
10 10
= 5 x 10-7
Part 3 Scientific Notation - How your calculator will give you an answer :the form is
(number bet 1 and 10 ) x ( power of 10 )
example
1900 x 1024
= 1.9 x 1027
Large numbers
NOT scientific notation
This is scientific notation
example
270,000,000
1. Put a pointer to the right of the first non zero digit
2. Count the spaces from the pointer to the decimal point
2^70,000,000
8
3. Replace the pointer with the new decimal point and
x 108
multiply by 10 power # places
If you move right from the pointer the power is
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Small numbers
example
0.0000075
1. Put a pointer to the right of the first non zero digit
0.000007^5
2. Count the spaces from the pointer to the decimal point
3. Replace the pointer with the new decimal point and
6
7.5
x 10-6
multiply by 10 power # places
If you move left from the pointer the power is
Practice
1. Write in scientific notation
a) 0.00567
- NEGATIVE
b) 5670
c) 0.0000000567
d) 86,700
2. Write in decimal form
a) 7.2 x 105
b) 2.88 x 10-4
ph 7 is neutral and the hydrogen ion concentration is 1 x 10-7
3. Chemistry
ph 5 is acid rain - the hydrogen ion concentration is 1 x 10-5
Acid rain has ________x more hydrogen ions than neutral water.
Part 4 Entering Scientific Notation with your calculator
First find the correct key Large numbers
ex
simple calculator EXP
or EE ( graphing calc 2nd EE)
1.75 x 1016
1. Enter the basic number
1.75
2. Hit the EE or EXP key
3. Enter the power
Small numbers
16
1.75 E 16
should appear or 1.75 x 1016
ex
6.67 x 10-11
(Hit CLEAR before you continue)
Casiofx300ms
Casiofx250hc
yours
Enter basic number
6.67
6.67
6.67
Hit spec key
EXP
EXP
Power
- 11
11 then (+/-) key
Display shows
** DO NOT **
enter 10
the EXP (EE) key knows you are doing powers of ten
** Older calculators - Do Not ** hit - before the power
- use (+/-) key
Practice 1. Interpreting your calculator - do on your calculator - write the answers in decimal form and scientific (3 sig figs)
b) (570,000)2
a) 1/3300000
2. In the USA cars drive 4 billion miles /day (4 x 10 9) and use over 200 million gallons of gasoline
a) what is the average miles/gallon
b) how much gasoline would be saved / day if the mileage was raised to 30 miles/gallon
c) how much oil would be saved?
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Part 5 Combining Numbers in Scientific Notation
a) Multiplying
to multiply two powers of 10
102 x 103
= 10 x 10
2
=
+ 3
add the powers
x
= 105
10 x 10 x 10
5
Practice
Set 1 - do by hand
1.
2 x 104
x
3 x 109
=
2.
3 x 10-12
x
2 x 10-4
=
3.
2 x 10-2
x
2 x 1016
=
Set 2 - do with your calculator
4.
2.08 x 104
x
3.12 x 109
=
5.
3.3 x 10-12
x
1.8 x 10-4
=
b) Dividing
to divide two powers of 10
subtract the powers
105 / 103
= 10 x 10 x 10 x 10 x 10
= 102
10 x 10 x 10
5
-
3
=
1.
3 x 1013 / 2 x 104
=
2.
2 x 1012 / 1 x 10-4
=
3.
6 x105
=
2
Practice
a) do by hand
/ 4 x 10-11
b) do these with your calculator
1.
3.08 x 1013/ 2.12 x 104
=
2.
3.95 x 1015/ 2.05 x 109
=
3.
2 x 1030
=
Sun Mass/ Earth Mass
4.
6 x 1024 / 7.4 x 1022
=
Earth Mass/ Moon Mass
/ 6 x 1024
6. General Practice
a) Physics Waves - for all types of waves the speed = wavelength x frequency
i) Red light waves have wavelength 6.0x 10-7 m , frequency 5.0 x 10 14 per sec. What is the speed?
ii) Radio waves have wavelength 100 m , frequency 3 x 106 per sec. What is the speed?
iii) What did you notice about these wave speeds?
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b) Environmental
i) In 2007 the world population was 7 billion ( 7 x 10 9) and the average CO2 production was 4.2 tons /person
Find the world total CO2
ii) Use the table to calculate the CO2 / person
Population
CO2
metric tons
China
1.34 billion
6.54 billion
USA
310 million
5.84 billion
Germany
81 million
787 million
for China , USA and Germany
iii) How does the USA CO2 rate compare with China,
Germany and the entire world?
CO2 per
person
c) Chemistry
i) 12 g of Carbon contains 6.02 x 10 23 atoms. How many atoms are in 240 g of carbon?
ii) 63 g of Iron has 6.02 x 10 23 atoms. How many atoms are in 6.3 kg of Iron ?
Part 7 Universal Gravitation Applications (p 180 Plug and Chug
Equation p 179 F =
1- 4)
G = 6.67 x 10-11
Explain each part of the equation
1. Calculate the force of gravity on
Mass of earth = 6 x 1024 kg
1 kg on the surface of the Earth
Earth radius = 6.4 x 106 m
2. Calculate the force of gravity on
Mass of earth = 6 x 1024 kg
1 kg twice as far from the center of the earth as #1
Earth radius = 6.4 x 106 m
distance for this problem =
3. Calculate the force of gravity between the earth and the moon
Mass of moon = 7.4 x 1022 kg
Ave distance Earth - Moon = 3.8 x 108 m
( Use mass of Earth from #1)
4. Calculate the force of gravity between the earth and the sun
Mass of sun = 2.0 x 1030 kg
Ave distance Earth - Sun = 1.5 x 1011 m ( Use mass of Earth from #1)
5. Which pulls the Earth more strongly, the sun or the moon ? (use your calculation results from above)
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