The Metric (SI) System

Unit 1

SI = Systeme Internationale

Used in Science Used throughout the

world (except in U.S.A.) for all measurements

Based on “10s”

Base Units Length = Meters (m) Mass = Grams (g) Volume = Liters (L) Temperature = Kelvins or Celsius

(based on absolute zero: -273ºC = 0 K)– 4 ºC = refrigerator– 20-22 ºC = room temperature– 37 ºC = body temperature

NOTE: base units do not get a prefeix!!

Metric Prefixes you MUST Memorize!!!!

Metric Prefixes To Memorize!!!Giga (G) 109

Mega (M) 106

Kilo (k) 103

Base Units – [m, L, g] 1Centi (c) 10-2

Milli (m) 10-3

Micro (µ) 10-6

Nano (n) 10-9

Measurements can be: Accurate – Close to the “true” value (with mutliple trials

compare the average to the true value) Precise – Reproducibility in replicate measurements (each

measurement is close to all of the others)

Neither accurate nor precise

Precise but not accurate

Precise AND accurate

Reading the Meniscus on a Reading the Meniscus on a graduated Cylindergraduated Cylinder

Always read volume from the bottom of the meniscus. The meniscus is the curved surface of a liquid in a narrow cylindrical container.

Try to avoid parallax errors.Try to avoid parallax errors.ParallaxParallax errorserrors arise when a meniscus or arise when a meniscus or needle is viewed from an angle rather than needle is viewed from an angle rather than from straight-on at eye level.from straight-on at eye level.

Correct: Viewing the meniscus

at eye level

Incorrect: viewing the meniscus

from an angle

Significant Figures. in Measurement

1. Identify the smallest unit that your device accurately measures to.

2. Estimate one digit past that smallest unit.– Ex. If the smallest division

is ones, you estimate to the 10ths.

52.8 mLMeasurement?

Reading the ThermometerReading the ThermometerDetermine the readings as shown below on Celsius thermometers:

. C . C 8 7 5 3 5 0

Your Turn:How many meters?

0.72 m

350 m

How many mL?

4800 mL

How many cm?

How many mm?

7.15 cm

71.5 mm

10 mL Graduate10 mL GraduateWhat is the volume of liquid in the graduate? (This one is tricky).

. mL6 6

25mL graduated cylinder 25mL graduated cylinder What is the volume of liquid in the graduate? . mL1 1 5

Practice

WS #1 -- Sig Figs in Measurement Metric Measurements Lab

Scientific Notation Why is Scientific Notation important?

– Make really big or really small numbers more manageable.– Helps keep track of significant figures.

In scientific notation, numbers are written as M x 10n. “M” must be a number between 0 and 10 (not including 0

or 10). Therefore, there must be one, and only one, number to the left of the decimal point; e.g., 2.35 x 105 meters.

156000 cm = 1.56 x 105 cm– Moving decimal left = (+) exponent– Multiplying by 105 = x 100,000

0.0000245 km = 2.45 x 10-5 km– Moving decimal to right = (-) exponent– Multiply by 10-5 = dividing by 100,000

Practice

Convert to or from scientific notation:1,4560.0034923.451 x 107

3.45 x 105

3.98 x 10-3

2.34 x 10-5

1.456 x 103

3.49 x 10-3

2.345 x 101

10,000,000

345,000

0.00398

0.0000234

Practice

WS #2 Scientific Notation

Significant Digits (Figures)

All non-zero digits are significant

9878 mL has 4 sig figs

Zeros appearing between non-zero digits are significant

403 L has 3 sig figs 504.07 L has 5 sig figs

Sig. Figs. (Cont.)

Zeros to the right of a non-zero digit and to the right of a decimal are significant

85.00 has 4 sig figs. 9.000000000 has 10 sig figs.

Zeros that appear in front of non-zero digits are not significant

0.095897 m has 5 sig figs

0.0009 Kg has 1 sig fig

Sig. Figs. (Cont.) Zeros at the end of a

number but to the left of a decimal may or may not be significant. If such a zero has been measured or is the first estimated digit, it is significant. If the zero has not been measured or estimated but is just a place holder, it is NOT significant.

2000 m may contain from 1 to 4 sig. figs depending on how many zeros are placeholders.

2000. definitely has 4, as indicated by the decimal.

This number can be rewritten in scientific notation to indicate any number of sig figs., e.g.:

2.0 x 103 has 2 sig figs

Sig. Figs, (Cont.)

Any counting numbers have an infinite number of significant digits.

250 cows has an infinite number of significant digits.

Conversion factors are never used to determine significant digits. E.g., 12 inches/1ft

How many sig figs in: 28.6 g 3340 cm 3340. cm 0.07080 m 9.8000 L 0.0067000 Kg 20 cars

3

4

3

5

5

Infinite – counting number

4

Practice

WS #3 – Significant Figures

Adding & Subtracting Sig. Figs. The answer must have

the same number of decimal places as there are in the measurement having the fewest decimal places.

Only adjust sig figs in your final answer

50.2 g – 32 g

57.712 57.71 g

44.15 44.2 L

4.8 ºC

18.2 18 g

25.652 g + 32.06 g = ?

42.1 L + 2.05 L = ?

36.6 ºC – 31.8 ºC

Multiplying & Dividing Sig. Figs. The answer can have

no more significant figures than are in the measurement with the fewest number of significant figures.

REMEMBER: Conversion factors are not significant!

50.2 g / 32 g

100,366 g 1.00 x 105 g

21.05 21.1 L

32.1552 x 108 m2 3.22 x 109 m2

1.56875 1.6 g

134 g x 749 g = ?

42.1 L / 2.00 L = ?

3.60 x 103 m x 8.932 x 105 m

Sig Figs in Combined Calculations In calculations that combine addition,

subtraction, multiplication, & division, sig figs are followed, but not included until the final answer.

Underline your sig figs in addition and subtraction to keep track

https://www.youtube.com/watch?v=__csP0NtlGI

Combined Example

Practice

WS #4 – Sig Figs in Calculations Metric Measurement Lab

Percent Error Calculation Measures how far off from the accepted

(theoretical) value the experimental value is.

%100Error %

lTheoretica

alExperimentlTheoretica

Percent Error Example:A student measures the mass and volume of a substance and calculates its density as 1.40 g/mL. The actual value of the density is 1.36 g/mL. What is the percent error of this measurement?

% Error = 1.36 g/mL - 1.40 g/mL X 100

1.36 g/mL

= 2.94% = 3%

Practice

WS #5 – Percent Error Calculations WS #6 -- #5 SciNotSigFig%Error Review