Units of Measurement SI units (Systeme Internationale d’Unites) were developed so that scientists could duplicate and communicate their work. Base UnitsDerived.

Units of MeasurementSI units (Systeme Internationale d’Unites) were developed so that scientists could duplicate and communicate their work.

Base Units Derived Units

Length meter (m) Volume meter cubed (m3)

Mass kilogram (kg) Densitygrams per cubic

centimeter (g/cm3)

Time second (s)

Temperature kelvin (K)

A unit that is defined by a combination of a base units.

Density

Ratio of an object’s mass to its volume

What happens to density when mass is constant and volume changes?

Volume

massDensity

Volume

massDensity

Mass, Volume and Density Relationships

Volume

Mas

s

Den

sity

Volume

DIRECT INDIRECT

Temperature Scales

273 CK

Reliability of Measurements

Accuracy vs. PrecisionHow close a measured value is to an accepted value

How close a series of measurements are to one another

High AccuracyLow AccuracyHigh Accuracy

High Precision

Low Accuracy High Precision

Percent Error

Used to evaluate the accuracy of experimental data.

alValueExperimentlueAcceptedVaError

100xlueAcceptedVa

ErrororPercentErr

Pre-Class Activity

602000000000000000000000

What is the significance of this number?

How would you express this number in scientific notation?

Scientific Notation

6.02 x 1023CoefficientExponent

The coefficient must be greater than or equal to one and less than 10.

When expressing numbers less than one (ex. 0.001) in scientific notation, the decimal point is moved to the right until the coefficient is within range. The number of spaces moved is used to determine the exponent.

For numbers less than one, the exponent is negative

When expressing numbers greater than 10 (ex. 1000) in scientific notation, the decimal point is moved to the left until the coefficient is within range. The number of spaces moved is used to determine the exponent.

For numbers greater than 1, the exponent is positive.

Scientific Notation CalculationsMultiplication and Division For multiplication, multiply the coefficients and add the exponents

(1.3 x 104) x (2.0 x 106) =

Remember, your final answer must be in the correct form. Often, multiplication of coefficients will yield a number greater than 10. In this case the result must be changed into the proper form.

(5.3 x 104) x (2.0 x 106) = =

For division, divide the coefficients and subtract the exponents. Often, division of coefficients will result in a value that is less than one. If this occurs, the final result must be changed into the proper form.

(2.0 x 10-3) (4.00 x 104) = =

2.6 x 1010

10.6 x 1010 1.06 x 1011

0.5 x 10-7 5 x 10-8

Scientific Notation Calculations

Addition and Subtraction In order to add or subtract numbers in scientific notation, the

exponents of each number has to be the same As a rule of thumb, it is best to take the number with the lower

exponent and change it match the higher exponent. To increase an exponent, move the decimal point in the coefficient

to left, the number of spaces equal to the increase in the exponent. Once the exponents are equal, the coefficients can be added or

subtracted

2.1 x 104

+ 1 x 103

2.1 x 104

+ 0.1 x 104

2.2 x 104

5.37 x 10-4

- 6.2 x 10-5

5.37 x 10-4

- 0.62 x 10-4

4.75 x 10-4

Pre-class Activity

How long is this paperclip? To what degree of certainty can it be measured?

Significant Figures in Measurement

Scientists determine the precision of instruments by the number of digits they report.

Significant Figures in Measurement

Measurements always include all certain digits and one uncertain digit.

52.7 mL

Measurement Challenge

What value would you assign to each of these measurements?

_________ mL

_________ cm

Identifying Significant Figures in Numbers

When examining a number, you determine the number of digits that are significant by the following rules:

1.All non-zero numbers are significant2.All final zeros to the right of a decimal are significant3.Zeros between significant digits are significant4.For positive numbers less than one, all zeros directly after

the decimal before the first significant figure are not significant.

5.All zeros at the end of a whole number are not significant.6.All contants and counting numbers have an unlimited

number of significant figures.

4.

5.

Sig Fig Challenge

How many sig figs are there in the following numbers:

1. 0.00042. 6873. 1.00824. 3305. 70.2080

Sig Fig Rules for Calculations

Multiplication and DivisionYour answer can not contain more or less sig figs than the operator that contains the least number of sig figs.

3.86 x 0.45=1.737 1.7

1.737Identify the significant figures, look on place beyond. If that digit is 5 or above, round up. If it is less than 5 drop off.

Sig Fig Rules for Calculations

Addition and Subtraction

Your answer can not be more precise than the least precise operator. Most of the time this means that your answer must have the same number of decimal places as the least precise operator

12.38 cm

+2.5 cm

14.88 cm 14.9 cm

1060 cm

+ 23.5 cm

1083.5 cm 1080 cm

If one of the numbers is a whole number that ends in zero(s), then the final answer must be rounded to the lowest place that contains a nonzero number.

Metric Conversions

mcdbdahK Move the decimal to the right

Move the decimal to the left

o Every metric unit is different from its neighbor by a factor of ten

o When converting between two units the decimal point is moved the number of places equal to the distance between the two unit in the chart above and in the same direction of movement

Sample problem

Convert the following 53 hg = ________dg

Start with 53.

Move the decimal 3 spaces to the right 53Fill in the empty spaces with zeros 53000 dg

mcdbdahK Move the decimal to the right

Move the decimal to the left

Sample Problem

Convert the following 300 cg = ________kg

Start with 300.

Move the decimal 5 spaces to the left 300Fill in the empty spaces with zeros 0.00300 kg

mcdbdahK Move the decimal to the right

Move the decimal to the left

More Practice Problems

Convert the following

0.058 dam = _______ dm

0.25 cL = _______ L

109 hg = ________ mg

mcdbdahK

5.8

0.0025

10900000

Factor Label Method of Conversion

Use conversion factors to systematically move from one unit to the next, cancelling out units on the diagonal in each step.

Convert 18 m = _______ cm

100 cm = 1 m 1 m = 100 cm 11

100

m

cm1

100

1

cm

m

18m100 cm

1 m= 1800 cm

Multistep Factor Label Problems

Convert

350 tsp = ______ L

Using the following conversion factors

1 tsp = 5 mL

1 L = 1000 mL

350 tsp 5 mL

1 tsp

1 L1000 mL

= 1.75 L

Multistep Factor Label Practice

Convert 3 min= ______ms

Use 1 min=60 s and 1000 ms = 1 s

Convert 32oz = _____ g

Use 16 oz=1 lb, 2.2 lb = 1kg, 1kg=1000 g

Multidimensional Factor Label Problems

Convert 25 g/mL = ______ kg/dL• Convert one unit at a time• Recognize that one unit is in the denominator

25 g

1 mL

1 Kg

1000 g

100mL

1 dL=2.5kg/dL

Multidimensional Factor Label Practice

Convert 85 km/hr = _________m/s

Convert 0.6 L/min = ________ qt/hrUse 1qt = 1.1L

Factor Label Practice for Area and Volume

1 ft = 12in

Remember to square or cube the unit as well as the number when converting to a squared or cubed unit

Representing Data

GraphingCircle Graphs (based on percents)

Bar Graphs (How quantities vary)

Graphing continued

Line Graphs In science, we draw a best fit line between data points.

Do not connect the dots.

Dep

ende

nt V

aria

ble

Dep

ende

nt V

aria

ble

Independent Variable Independent Variable

Which graph shows and indirect relationship between the dependent and independent variable?

Calculating the Slope of a Best Fit Line

Select two points on the line that you have drawn. Do not select two of your data points because they might not fall on the line.