DO NOW!

• Metric system is based on powers of 10• Standard units in the metric system are meter, liter,

gramPrefixes

• The two methods of converting between units within the metric system include the ladder method (moving decimal place), and using conversion factors.

kilo hecto decameterlitergram

deci centi milli

Take out your SI Conversion notes from last week. Complete page 1 using this slide.

KILO1000Units

HECTO100

UnitsDEKA

10Units

DECI0.1

UnitCENTI

0.01Unit

MILLI0.001Unit

MetersLitersGrams

Ladder Method

How do you use the “ladder” method? 1st – Determine your starting point.

2nd – Count the “jumps” to your ending point.

3rd – Move the decimal the same number of jumps in the same direction.

4 km = _________ m

12

3

How many jumps does it take?

Starting Point Ending Point

4.1

__.2

__.3

__. = 4000 m

Standard

The Conversion Factor Method

The following are common metric system equations that can be used as conversion factors to cancel out units.

1 m = 100 cm 1000 mL = 1 L1 kg = 1000 g 1 g = 1000 mg

Example: Using Conversion Factors

How many milliliters are in 15.67 L of water?

Given: 15.67 L of waterNeeded: mL of water

𝟏𝟓 .𝟔𝟕𝐋𝟏 ∙𝐦𝐋𝐋

1000 1

15,670 mL

Significant Figures

2-3 Scientific Measurement

Error in Measurement

• Some error or uncertainty always exists in any measurement.

• The measuring instruments themselves place limitations on precision.

• All measurements in science should have ONE uncertain or estimated digit (always the last number)

Example:

• The following picture represents a graduated cylinder with water in it.

• The meniscus lies between 44mL- 45mL, therefore an accurate volume would be 44._ mL

• You would make an estimate as to what the last digit should be.

• Perhaps 44.5 mL

Example:

• The following picture represents a metric ruler measuring a pencil.

• The pencil tip lies between 8.2 cm - 8.3 cm, therefore an accurate length would be 8.2_ cm

• You would make an estimate as to what the last digit should be.

• Perhaps 8.23 cm.

cm

You Try It! - Practice Problems

SIGNIFICANT FIGURE RULES1. Any non-zero number is ALWAYS

significant. 28.49

2. Any zero(s) between two significant numbers is ALWAYS significant. 505.7009

3. Any placeholder zero(s) (leftmost zeros), is NEVER significant. 0.00896

SIGNIFICANT FIGURE RULES4. Any zero(s) at the end of a number

AND to the right of a decimal is ALWAYS significant. 943.8900

5. Any zero at the end of a number AND to the left of a decimal is NEVER significant UNLESS there is an obvious decimal. 980 980.

SUMMARY OF SIG FIG RULES

• ALL numbers are considered significant EXCEPT:

Zeros that start a number Zeros that end a whole number (no decimal)

0.008764 6,745,000

YOU TRY IT!How many significant figures are

in the following measurements?Put the Rule #(s) that you followed to get to your answer.

1. 15.39 2. 9.078003 3. 4.0800 4. 23190

Practice Problems

45.87360.000239 0.00023900 48000. 48000 3.982106 1.000401.50 x 103

63552463

•All digits count

•Leading 0’s don’t

•Trailing 0’s do

•0’s count in decimal form

•0’s don’t count w/o decimal

•All digits count

•0’s between digits count as well as trailing in decimal form•Trailing 0’s do

MULTIPLYING AND DIVIDING WITH SIGNIFICANT FIGURES

a. 4.0 5 =

b. 4.00 5.0 =

c. 4.000 5.00 =

2 1 1

3 2 2

4 3 3

MULTIPLYING AND DIVIDING RULE

• The final answer should be rounded to the same number of significant figures as the measurement with the least number of significant figures in the problem.

ADDING AND SUBTRACTING WITH SIGNIFICANT FIGURES

a. 4.4 + 5 =

b. 4.02 + 5.0 =

c. 4.006 + 5.00 =

1 0 0

2 1 1

3 2 2

ADDING AND SUBTRACTING RULE

• The final answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places in the problem.

CONVERSION FACTORS

• Conversion factors are exact numbers and therefore have an infinite number of significant figures.

• When doing conversions, your final answer should have the same number of significant figures as the given number.