Name: ________________________________ Date: _____________________ Period: _______
Activity: Ratios and Scientific Notation
Notes:
What are ratios?
How are they used?
Ratios are ______________, and the word “per” means ______ _______.
Scientific Notation is ___________________________________________
Part 1
Example: A truck requires 3L of gasoline to travel 15km, how many km can
the truck travel on 1L of gas?
Ratios are useful when making comparison. Use ratios to compare the
number of miles each vehicle can travel using one gallon of gas.
1. A sports car uses 0.8 gallons of gas to travel 57 miles, how many
miles per gallon does it get?
2. An SUV uses 3.9 gallons of gas to travel 57 miles, how many miles
per gallon does it get?
3. How many gallons of gas does the sports car require to travel 250
miles?
Name: ________________________________ Date: _____________________ Period: _______
Part 2
Ratios can also be used to convert from one unit to another unit!!!
You will be using the blue balances, chips, washers, and nuts in this part
to balance, create conversion factors, and solve problems!
1. How many chips are required to balance one washer? _________
2. Write the number of chips per washer as a ratio.
_________
3. How many chips are required to balance one nut?
_________
4. Write the number of chips per nut as a ratio?
_________
5. Without using the balance, calculate how many nuts it would take
to balance one washer. Use conversion factors and show your
work.
6. Use the balance to check your answer to #5. How many nuts
balanced one washer?
_________
7. List three common ratios.
8. Why are ratios useful? __________________________________
_____________________________________________________
_____________________________________________________
Name: ________________________________ Date: _____________________ Period: _______
Part 3:
How are ratios used to calculate efficiency:
Efficiency is
____________________________________________________________
____________________________________________________________
Efficiency = ____________________ x100
Example: What is the efficiency of a process that requires 600 Joules of
energy to produce 200 Joules of energy?
Procedure: Connect one hand-crank generator to a second hand-crank
generator. Turn the crank of the first generator slowly 10 full revolutions.
1. How many revolutions did the handle of the second generator turn?
_______
2. Calculate the efficiency of the system of two generators when the first
generator crank is turned slowly. (Show your work).
_______%
3. Now turn the first generator’s handle rapidly 10 full revolutions. How
many revolutions did the second generator’s handle turn?
_________
Calculate the efficiency when the second generator handle is turned
rapidly.
_______%
4. Why might the efficiency depend on the speed that you turn the handle?
_________________________________________________________
_________________________________________________________
5. Is it possible to turn the handle rapidly enough so that the second handle
also turns 10 revolutions? Explain: _____________________________
_________________________________________________________
Name: ________________________________ Date: _____________________ Period: _______
Part 4
1. How do exponents and scientific notation simplify calculation?
_________________________________________________________
_________________________________________________________
Joe says that 22 x 23 = 22x3, but Shannon says that 22 x 23 = 22+3. To decide
who is correct, answer these questions!
2. How much is: 22 = _______, 23 = _______, 22 + 23= _______
3. How much is: 22x3 = _______, 22+3 = _______
4. Based on these results, whose method is correct?
__________
5. State a rule for multiplying numbers with exponents.
_________________________________________________________
_________________________________________________________
_________________________________________________________
6. Apply your rule to calculate 103 x 102 = __________________________
Sarah says that 106/102 = 106/2, and Jack says that 106-102 = 106-2. To
decide who is correct, answer these questions!
1. How much is: 106 = _______, 102 = _______, 106/102 = _______
2. How much is: 106/2 = ______, 106-2 = _______
3. State a rule for dividing numbers with exponents.
_______________________________________________________
_______________________________________________________
_______________________________________________________
Name: ________________________________ Date: _____________________ Period: _______
Solve the following problems. Write your answer in scientific notation!!!
1.
2.
3.
4.
5.
(5x101) x (3x102)
(7x103) x (1x10-2)
1010/105
(8x106)/(2x103)
(6x103)/(2x105)
= __________
= __________
= __________
= __________
= __________
Part 5
Look at the table of the energy content found in some common fuels. Use
this information, along with ratios and scientific notation, to convert the
following units.
1. How many kg of wood are needed to produce the same amount of
energy as 1kg of coal?
2. How many kg of crude oil are needed to produce the same amount of
energy as 1kg of uranium235?
Type of Fuel
Coal
Crude Oil
Gasoline
Natural Gas
Wood
Assorted Garbage and Trash
Bread
Butter
Nuclear Fission with Uranium 235
Energy in joules/kg of Fuel
2.9x107
4.3x107
4.4 x107
5.5 x107
1.4 x107
1.2 x107
1.0 x107
3.3 x107
8.0 x1013