The Metric System

“I’m ten times better than the

Standard system of measurement!”

Metric System

Many laboratory activities require measurements.

Science uses the S.I. (Metric System) of measurements.

Measurements in ExperimentsMetric System

• Developed by the French in the late 1700’s.• Based on powers of ten, so it is very easy to

use.• Used by almost every country in the world,

with the notable exception of the USA.• Especially used by scientists.

• Called the International System of Units or in French the Le Système International d'Unités abbreviated SI.

Metric Prefixes

• Regardless of the unit, the entire metric system uses the same prefixes.

• Common prefixes are:kilo = 1000centi = 1/100th

milli = 1/1000th

pico = 1/1000,000,000,000 or 1 x 10 -12

1 meter = 100 centimeters =1000 millimeters

Length• The SI base unit for length is the meter (m)

• Common units for length – millimeter, centimeter, meter or kilometer

• Abbreviated (mm, cm, m, km)

Mass• The SI unit for mass is the kilogram (kg)• Balances are used to determine mass. • Common units of mass: gram (g), milligram

(mg), kilogram (kg)

Your mass in Kg? 1 kg / 2.2 lbs

Electronic BalanceTriple Beam Balance

Temperature

•The Kelvin (K) is the SI unit for temperature

•Celsius (0C) is the metric unit for temperature

•O 0 Celsius = 273 K

Know the temperature at which water freezes and boils in the 3 different temperature scales:

temperature kelvin degree Celsius degree Fahrenheit

symbol K °C °F

boiling point of water 373.15 100. 212.

melting point of ice 273.15 0. 32.

absolute zero 0. -273.15 -459.67

Volume• Units of volume are derived

from units of length.

Formula:Volume = length x width x

height

• The metric units of volume are cubic centimeters (cm3)

• A box 2 cm x 3 cm x 5cm has a volume of __________ ?

• 30 cm3

Liquid Volume

• Graduated Cylinder used to measure volume

• 1 cm3 of water is equal 1 milliliter (ml) of water and 1 ml of water will always have a mass of one gram.

1 cm3 of anything = 1 mL of anything

1 cm3 water = 1 mL of water = 1 gram

Meniscus – the ‘bubble’ that form on the wall of the glass. Always read from the bottom of the meniscus

Water Displacement

• Water displacement is used to find the volume of objects that are not boxed shaped. (irregular shaped objects)

• Example: 50-mL of water is placed in a graduated cylinder.

• If a rock causes the level to rise to 73-mL, the rock must have a volume of 23-mL.

• 73 – 50 = 23 mL

To Convert Measurements use Dimensional Analysis by multiplying by a conversion factor: a factor equal to one.

Example: To convert 56 m to km -- 56 m x 1 km = 0.056 km

1000 m

Example: Convert 65 miles per hour (mph) to km/hr

65 mi/hr x 1.61 km/hr 1 mi /hr

= 104 km/hr

Accuracy and PrecisionAccuracy – describes how close a measurement is to the true value of the quantity measured.Precision – the exactness of a measurement Example: 45.052 m is more precise than 45.0 m

Low AccuracyHigh Precision

High AccuracyLow Precision

High AccuracyHigh Precision

So, if you are playing soccer and you always hit the left goal post instead of scoring, then you are not accurate, but you are precise!

Significant FiguresUsed to show the precision of a measured quantityInclude all digits that are actually measured plus one estimated digit.

Rules: 1) All non zero number are significant

738 = 3 sig figs12345 = 5 sig figs

2) Zeros located between non-zero digits are significant 2012 = 4 sig figs

This measurement should be read as 4.95 cm. This measurement has 3 significant figures.

3) Trailing zeros (at the end) are significant only if the number contains a decimal point; otherwise they are insignificant (they don’t count)

1.00 = 3 sig figs549000. = 6 sig figs549000 = only 3 sig figs

4) Zeros to the left of the first nonzero digit are insignificant (they don’t count); they are only placeholders.

000.456 = 3 sig figs0.052 = 2 sig figs

Rules for addition/subtraction problemsThe number of decimal places in the result equals the number of decimal places in the least precise measurement

Example: 7.939 + 6.26 + 11.1 = 25.299

Answer = 3 sig figs 25.3 (rounded up)

Rules for multiplication/division problemsThe number of sig figs in the result equals the number in the least precise measurement used in the calculation

Example: (27.2 x 15.63) ÷ 1.846 = 230.3011918

Answer = 3 sig figs 230. (rounded down)

Estimating the last digit in a measurement This measurement should be read as 4.95 cm. This measurement has 3 significant figures.

Reading a metric ruler correctly:

This point can be read as 1.65 cm. or 16.5 mm.

Density• Density - the amount of matter (mass) compared to

the amount of space (volume) the object occupies.

• Density – Is a Physical Property of matter - it is a constant, a number that does not change.

Example: Density of Gold = 19.30 g / ml

Question: If you cut a brick of gold in half would the Density still be 19.30 g/ml?

Yes…. Why?

Formula

Density = mass/volume D = M / V

•The unit for mass is grams (g), and the unit for volume is mL or cm3 usually,

so the units for Density are g/mL, or g/cm3

Density Formula Wheel

• Formula wheels make it easy to solve density problems.

• Cover the property you are trying to find, and do what is left over.

• To find density, cover the word density. You have mass over volume remaining. So divide mass by volume to find density!

Mass

density

volume

Density Formula Wheel

• To find mass, you cover the word mass. You now have density times volume remaining.

• To find volume, cover volume. You have mass over density remaining, so divide mass by density to find volume.

Mass

density

volume

Understanding Density• In the following illustrations, each will

represent 1 cm3.• Each g will represent 1 gram.• Mass = 24g• Volume = 8 cm3

• Density = 3g/cm3 g g g

g g g

g g g

g g g

g g g

g g g

g g g

g g g

g g g

g g g

g g g

g g g

g g g

g g g

g g g

g g g

•In other words, there are 3 grams in every cmcm33..

Density Problem 2

g g

g g g g

g g

g g

g g

•Mass = 12 grams

•Volume = 6 cmcm33

•Density = 2 g/cm3

•In English we say the density of the object is 2

grams in every cubic centimeter.

Density Problem 3g

g g g

g g g

g g g

g g g g g

g

•Our previous problems were materials of uniform density. They were the same stuff throughout. But many materials are not. Gravel is a great example.

•Mass = 16 grams

•Volume = 8 mL

•Density = 2 g/mL

http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

Powers of Ten Interactive Tutorial

http://www.onlineconversion.com/length_common.htm

How to Convert Metric UnitsSee link below for an online calculator

•To convert to larger unit (example: meter to a kilometer), move the decimal point to the left or divide.

•To convert to a smaller unit (example: meter to centimeter), move the decimal point to the right or multiply.

Example: to convert 100 g to kilograms move the decimal place 3 places to the left (or divide by 1000).

Answer: 0.100 kg