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) (Book says kg) 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

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 Precise – Reproducibility in replicate

measurements

Neither accurate nor precise

Precise but not accurate

Precise AND accurate

Reading the MeniscusReading the MeniscusAlways 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

Sig. Figs. in Measurement1. Identify the smallest unit

that your device accurately measures to.

2. Estimate one digit past that smallest unit.

If the smallest division is tenths, you estimate to the 100ths. If it is to the ones, estimate to the tenths.

Use the graduations to find all Use the graduations to find all certain digitscertain digits

There are two unlabeled graduations below the meniscus, and each graduation represents 1 mL, so the certain digits of the reading are…

52 mL.

Lab techniques lab

Estimate the uncertain digit and Estimate the uncertain digit and take a readingtake a readingThe meniscus is about eight tenths of the way to the next graduation, so the final digit in the reading is _______.

The volume in the graduated cylinder is

0.8 mL

52.8 mL.

10 mL Graduate10 mL GraduateWhat is the volume of liquid in the graduate?

. mL6 6

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

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

Practice

WS #1 -- Sig Figs in Measurement

Scientific Notation In scientific notation, numbers are written as

M x 10n. “M” must be a number between 0 and 10. 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 0.0000245 km = 2.45 x 10-5 km If you move the decimal point to the left, you

add to the exponent. (Remember: LA) Scientific Notation helps keep track of

significant figures!!!

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.

E.g. 2.0 x 103 m has 2 significant digits.

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

5.44000 g /8.100 mol

2.8297 2.83 m

27.974 27.97 g

1.003392 1.00 mm

44.064 44.06 g/mol

5.44 m – 2.6103 m

2.654 g + 25.32 g

1.34 mm x .7488 mm

Practice

WS #3 – Significant Figures

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.

Adding & Subtracting Sig. Figs. When adding or

subtracting decimals, the answer must have the same number of decimal places as there are in the measurement having the fewest decimal places. 50.2 g – 32 g

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. When multiplying or

dividing decimals, 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

Practice

WS #4 – Sig Figs in Calculations

Percent Error Calculation The accuracy of an individual value or of an

average experimental value can be compared quantitatively with the correct or accepted value by calculating percent error.

Percent error is calculated by subtracting the experimental value from the accepted value, dividing the difference by the accepted value, and then multiplying by 100. Percent error is always the absolute value of your answer.

Percent Error Formula

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– Don’t forget significant figures!!!