Ch 5: Measurements and Calculations

I. Scientific Notation and Units

A. Scientific Notation: A way to easily show lengthy numbers.

1. M x 10n where 1 < M < 10 and n = decimals to

move.a) Move decimal till number is between 1 and 10b) Determine the exponent (n)

– Positive n = moved to the left– Negative n – moved to the right

The Sun is 93,000,000 miles away if you travelled 5000 miles per hourhow many hours would it take to reach the sun?How many days would it take to reach the sun?How many years would it take to reach the sun?

12 grams of carbon has 602,200,000,000,000,000,000,000 atoms in it.If a pile of carbon weighs 41 grams, how many carbon atoms are in the pile?

A different way to show a number

4.3 x 10 =

4.3 x 10 x 10 =

4.3 x 10 x 10 x10 =

Every time you multiply by 10 it moves the decimal to the right 1 spot.What’s the rule this shows?

4.3 / 10 =

4.3 /10/10 =

4.3 /10/10/10 =

What’s the rule this shows?Every time you divide by 10 it moves the decimal to the left 1 spot

Scientific Notation Practice• Change the following to Scientific Notation

1. 93142. 0.080423. 0.00005174. 7,124,369,582

• Change the following to standard numbers.1. 4.17 x 104

2. 6.19 x 10 -2

3. 3.001 x 10-5

4. 5.91 x 10 7

B. Units: Indicator of what scale is used for measuring.1. International System of Measurement (SI)

a. Mass = The quantity of matter in an object = Grams (g)b. Length = Meters (m)c. Time = Seconds (sec)d. Temperature = Kelvin (K)e. Volume = 3 dimensional space taken up = Liter (L)

C. Use prefixes to make numbers usable (verbal multiplier)

Converting Metric Prefixes.1. Determine the difference between the

exponent for each unit.2. Move the decimal that many places.• If going down the table, move right.• If going up the table move left. Convert The following

5.45kg g

6.19nm m

4.90 x 107 µL kL100

Base Unit -g -L -m µ

1.34 x 10-5 ML L

II. Uncertainty in Measurments

A. All measurements have an estimated digit.1. Determine the smallest digit that is indicated on

the device, and estimate one digit farther.

B. Significant Figures: The numbers that were actually recorded in a measurement.

1. Rules for counting Significant Figures:a. Nonzero’s are significantb. Final zero’s after the decimal are significantc. Zero’s that are between other significant figures are

significant.

Pg 146 Example 5.3 a-d

How many significant figures are in each of the following numbers?

1) 0.00240g2) 1.002403) 1000L4) 1000.0L

C. Exact Numbers: numbers determined by counting.1. have unlimited significant digits.

Pg 146 Practice Problem Exercise 5.3 a-c

D. Significant Figures in Calculations: (How many digits should I keep in my answer?)

1. Addition or subtraction:The answer may hold as many decimal places as the number

from the problem that has the least decimal places. (round to that place value)

2. Multiplication or Division:The answer may hold as many significant figures as the

number from the problem that has the least significant figures. (round to that number of significant figures.

12.11g + 18.0g + 1.013g = 31.123g

4.56 m x 1.4m = 6.384m2Pg 149 Practice Problem Exercise 5.5 a-c

183.062km – 14km = 169.062km

353.2mL + 17.89 mL= 371.09mL

4.87m / 8.73g x 13m = 7.252 m2/g

8.315g / 298L = 0.0279027g/LPg 150: 5-7

5. How many sig. fig. should be in each resulta) 2 c) 2b) 1 d) 3

6. Resultsa) 5.4 c) 5.0 x 107

b) 100 d) 885007. Number of sig. figs in a measurement.

a) 2 (example is 14)b) 3 (example is 3.14)c) 2 (example is 4.6)

III. Problem Solving and Unit Conversions

A. Problem Solving:1. Where do we want to go? What is the problem

asking for?2. What do we know? List of facts.3. How do we get there? What steps can we take to

solve the problem.4. Does it make sense? Evaluate if the answer is

reasonable

You need two dozen doughnuts for advisory groups. Dunkin Donuts sells doughnuts for $0.50 each. How much will the doughnuts cost?

Algebra Review

1. What’s the rule?Anything divided by itself = 1

Algebra Review

1. 5 • 1 = 2. 17 • 1 =3. 1.456 • 1 =4. 1,346,000.309534 • 1 =5. x• 1 =6. What’s the rule?

Anything multiplied by 1 stays the same.

Algebra Review

1. =2. =3. • =4. 45x • =

B. Converting Units of Measure: Changing the units of a measurement but keeping the value the same. 1. Equivalence Statement: Shows two different #’s that

are the same value. (2.45cm = 1 in.) See pg 1532. Conversion Factors: A ratio that relates two units.

a. They are made from the 2 parts of an equivalence statement.» or

b. A conversion factor allows us to cancel out a unit and replace it with new unit.

Practice Problem 5.6 pg 156

You need two dozen doughnuts for advisory groups. Dunkin Donuts sells doughnuts for $0.50 each. How much will the doughnuts cost? (show using unit conversion)

3. How to use a conversion factor to do a conversiona. Identify the equivalence statement(s) that will help with this

problem.b. Write the number and unit given in the problem.c. Multiply by a conversion factor (fraction) where

• The bottom has the unit you want to get rid of. (so it cancels out)

• The top has the unit that you want to end up with.d. Do the appropriate math.e. Make sure you have the correct number of significant

figures. (look at the original measurement to determine sig. figs.)

Use Table 5.7 to make the following conversion.

Convert 3.79kg to lbs.

Use Table 5.7 to make the following conversion.

Convert 35.7qt to L

Use Table 5.7 to make the following conversion.

Convert 2.37mi to m.

Pg 170:2-4

Conversion Factors and metric Prefixes.

100

µ

1111111

1 M__ 106 __

1 k__ 103 __

1 d__ 10-1 __

1 c__ 10-2 __

1 m__ 10-3 __

1 µ__ 10-6 __

1 n__ 10-9 __

=======

Convert 35mg to gConvert 7.38m to Mm

Convert 41.9kL to dL

C. Temp. Conversions1. Celsius Scale: Based on the freezing and boiling point

of water Tf = 0 oC Tb = 100oC

2. Kelvin Scale: Base on absolute zero as the coldest temp.

Tf = 273K Tb = 373K 3. Conversions:

a. C K add 273 to the celcius temperature. b. K C subtract 273 from the kelvin temperature.

143o C to K

Complete the following conversions

199K to o C -215o C to K198K to o C

D. Density: The amount of matter present in a given volume of a substance.1. Mass per unit of volume ()2. The density of a type of material is always the same. (ie. The

density of copper is 8.92g/mL)• D = m = mass (g)

D = Density,V = volume (mL or cm3 )

1. Use this equation to determine the density, mass, or volume of an object.

Density Problems

If a block of stone has a mass of 45.3g and takes up a volume of 100.4mL, what is its density?

The density of a rock is 0.9980g/mL. What is the mass of the rock if the volume is 345mL?

The density of a piece of metal is 1.113g/mL. What is the volume of a piece of metal with a mass of 1.45kg?