Download 20 nickels = 1 dollar

DIMENSIONAL ANALYSIS – STEPS TO CONVERT UNITS
Dimensional Analysis (Factor Label)
Using equivalent relationships to obtain unit conversion factors that help you solve a problem.
Unit Conversion Factors – a ratio of two quantities that are equivalent and are used to
convert from one unit to another. Two examples of the same conversion factor is shown below:
1 dollar
100 pennies
100 pennies
1 dollar
To Solve:
1. Look at what is given in the problem.
2. Look at what is being asked in the problem (answer should be in, what units?).
3. Look for unit conversion factors to get from what is given to what is asked for.
4. For each step, arrange unit conversion factor so that the denominator of your
conversion factor is what unit you are starting with, and the numerator is what you
are ending with:
numerator: what units you want to end with
denominator: what units you start with
5. Use a solution map to visualize the route required to solve the problem
Starting Units --------------------> Steps ------------> Ending Units
Example 1:
How many dollars is 5,000 nickels?
 ANSWER SHOULD BE IN WHAT UNITS? -------------------------------“dollars”
 HOW MANY NICKELS (what we start with) IS EQUAL TO A DOLLAR (what we end with)

20 nickels = 1 dollar ; We must decide which conversion factor to use below:
20 nickels
1 dollar
and
1 dollar
20 nickels
Use this one because it has the units our answer
should be in “dollars” in the numerator!!
numerator: what units you want to end with
5,000 nickels x $1.00 (dollar)
20 nickels
=
$250!!
denominator: what units you start with
Example 2:
How many nickels is $12,480?
Use other conversion factor because it has the units our answer should be in “nickels”
in the numerator!!
$12,480 x 20 nickels = 249,600 nickels!!
numerator: what units you want to end with
$1.00(dollar)
denominator: what units you start with
Dimensional Analysis Worksheet
Name___________________________
1.
Convert 42 centimeters to inches. (2.54 centimeters = 1 inch)
2.
Convert 50 milliliters to liters. (1000 milliliters = 1 liter)
3. Convert 285 grams to pounds. (454 grams = 1 pound)
4. How many minutes are there in 3 hours?
5. How many minutes are there in 3 days?
6. If you are 2.3 meters tall, what is your height in inches? (39.37 inches
= 1 meter)
7. A flea wing weighs 0.00000703 pounds. How many milligrams does it weigh? (1 pound =
454 grams, 1000 milligrams = 1 gram) (Try to answer this one using scientific
notation)
2
8. Convert 1.2 x 10 nm to km.
9. If an airline charges 16 cents per mile, how many miles can you travel for $80?
Name
Date
Class
Math Skills for Science
MATH SKILLS
Multiplying and Dividing in Scientific Notation
Part 1: Multiplying in Scientific Notation
PROCEDURE: To multiply numbers in scientific notation, multiply the decimal
numbers. Then add the exponents of the powers of 10. Place the new power of
10 with the decimal in scientific notation form. If your decimal number is
greater than 10, count the number of times the decimal moves to the left, and
add this number to the exponent.
SAMPLE PROBLEM: Multiply (2.6 ⫻ 107) by (6.3 ⫻ 104).
2.6 ⫻ 6.3 ⫽ 16.38
7 ⫹ 4 ⫽ 11
Step 3: Put the new decimal
number with the new exponent in
scientific notation form.
Step 4: Because the new decimal number is
greater than 10, count the number of places
the decimal moves to put the number
between 1 and 10. Add this number to the
exponent. In this case, the decimal point
moves one place, so add 1 to the exponent.
16.38 ⫻ 1011
1哬
6.38 ⫻ 1011 → 1.638 ⫻ 1012
Try It Yourself!
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. Follow the steps in the Sample Problem carefully to complete the following equations.
Multiplying with Scientific Notations
Problem
Sample problem:
(4.4 ⫻ 106) ⫻ (3.9 ⫻ 104)
New decimal
New exponent
Answer
4.4 ⫻ 3.9 ⫽ 17.16
6 ⫹ 4 ⫽ 10
1.716 ⫻ 1011
a. (2.8 ⫻ 108) ⫻ (1.9 ⫻ 104)
b. (1.3 ⫻ 109) ⫻ (4.7 ⫻ 10⫺5)
c. (3.7 ⫻ 1015) ⫻ (5.2 ⫻ 107)
d. (4.9 ⫻ 1024) ⫻ (1.6 ⫻ 105)
2. The mass of one hydrogen atom is 1.67 ⫻ 10 –27 kg. A cylinder contains 3.01 ⫻ 1023
hydrogen atoms. What is the mass of the hydrogen?
1 of 2
MATH SKILLS
Step 2: Add the exponents.
▼
▼
▼
Step 1: Multiply the decimal
numbers.
Name
Date
Class
Multiplying and Dividing in Scientific Notation, continued
Part 2: Dividing in Scientific Notation
PROCEDURE: To divide numbers in scientific notation, first divide the decimal
numbers. Then subtract the exponents of your power of 10. Place the new power
of 10 with the decimal in scientific notation form. If the resulting decimal
number is less than 1, move the decimal point to the right and decrease the
exponent by the number of places that the decimal point moved.
SAMPLE PROBLEM: Divide (1.23 ⫻ 1011) by (2.4 ⫻ 104).
Step 1: Divide the decimal numbers.
Step 2: Subtract the exponents of the
powers of 10.
1.23 ⫼ 2.4 ⫽ 0.5125
11 ⫺ 4 ⫽ 7
Step 3: Place the new power of
10 with the new decimal in scientific
notation form.
Step 4: Because the decimal number is
not between 1 and 10, move the decimal
point one place to the right and
decrease the exponent by 1.
0.5125 ⫻ 107
0.5 125 ⫻ 107 → 5.125 ⫻ 106
哬
(1.23 ⫻ 1011) ⫼ (2.4 ⫻ 104) ⫽ 5.125 ⫻ 106
3. Complete the following chart:
Problem
Sample problem:
(5.76 ⫻ 109) ⫼ (3.2 ⫼ 103)
New decimal
New exponent
Answer
5.76 ⫼ 3.2 ⫽ 1.8
9⫺3⫽6
1.8 ⫻ 106
a. (3.72 ⫻ 108) ⫼ (1.2 ⫻ 105)
b. (6.4 ⫻ 10⫺4) ⫼ (4 ⫻ 106)
c. (3.6 ⫻ 104) ⫼ (6 ⫻ 105)
d. (1.44 ⫻ 1024) ⫼ (1.2 ⫻ 1017)
4. The average distance from Earth to the sun is 1.5 ⫻ 1011 m. The speed of light is
3 ⫻ 108 m/s. Approximately how long does it take for light to travel from the sun
to Earth?
2 of 2
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Dividing with Scientific Notation
Intermediate Algebra Skill
Multiplying and Dividing Using Scientific Notation
Simplify. Write each answer in scientific notation.
−6
1) (8.18 × 10
3) (0.8 × 10
4
5) (1.9 × 10
−3
7)
9)
11)
7.8 × 10
)(1.15 × 10 −5 )
)(1.28 × 10 6)
)(2 × 10 4 )
−6
)(2 × 10 4 )
4) (3.8 × 10
−6
)(2.37 × 10 −3 )
6) (9.2 × 10
5
5.3 × 10
3
4
8)
8 × 10 1
4.6 × 10
2
10)
5.01 × 10 −3
5.5 × 10
−1
5.3 × 10
12)
2
13) (7.87 × 10
15) (4 × 10
2) (5.8 × 10
−1 −6
)
1 −5
)
4
19) (6.9 × 10 −6 )(770 × 10 2 )
1
7.65 × 10 5
7.6 × 10
0
5.4 × 10 −6
2.04 × 10
2 × 10
−1
−2
14) (9.1 × 10
−5 −4
)
16) (2.19 × 10
17) (9.7 × 10 −3 )
21) (0.95 × 10
)(4 × 10 −3 )
)(0.4 × 10 −2 )
23) (5.32 × 10 1 )(2.21 × 10 1 )
4 −6
18) (5.9 × 10 0 )
)
−2
20) (7.57 × 10 −4 )(8.8 × 10 −1 )
22) (12 × 10
5
)(2 × 10 2)
24) (8 × 10 −4 )
6