Measurement and Dimensional Analysis

The Importance of Measurement

A. Measuring is a fundamental skill of science.

B. Without measurements we could not describe our observations.

Measurements provide a standard.

A. Two types of measurement1. Quantitative measurements- give results in

a definite form, usually as numbers.ex: “The car weighs 2000 kg.”

2. Qualitative measurements- give results in a descriptive nonnumeric form.ex: “The car is blue.”

The Metric System

A. Although the United States still uses the English system of measurement, the rest of the world has switched to a standard form of measurement known as the metric system.

What metric units do you know?

A. Give a metric unit of measurement for the following quantities:

1. Mass

2. Temperature

3. Volume

4. Time

Base Units in the Metric System

A. Base units are defined based on something observable object or event in the world

1. length- meter(m)2. mass- gram(g)3. time- second(s)4. electric current – ampere(A)5. temperature – celsius (C)6. amount of substance – mole (mol)7. luminous intensity – candela (cd)

Derived Units in the Metric System

A. A derived unit is a combination of base units, and sometimes other derived units

1. Volume: Liter (L)a) 1 L = 1000ml = 1000 cm3

2. Density: grams per cubic centimeter ( g/cm3 )

3. Force: Newton (N) = 1 kg m/s2

4. Energy: joule (J) = 1Nm

Using Measuring Tools in Science

A. You must always read the scales on equipment one place past the last mark.

Examples

A. What is the volume of the following liquids.

A. Determine the mass of the object on the balance.

Measuring MatterMass

1. Measurement of the quantity of matter in an object

2. Ex) golf ball = mass = 45 g, tennis ball = 2.5 g

Density3. Mass and volume can be used to find density

4. D = m/v

5. Ex) mass = 10 g volume = 2 cm3

10 g = 5 g/cm3

2 cm3

Measuring DistanceLength

1. Distance between two points

2. Ex) diameter of a hair, distance from Earth to the Moon

3. SI unit length = meter (m)

4. The unit for measure depends on what you are measuring

a) Ex) cm – pencil m – classroom km – school to home

b) By choosing appropriate units you avoid large digit numbers

Measuring VolumeVolume

1. amount of space occupied by an object

2. v = l x w x ha) Multiply 3 numbers and units together

b) Ex) a cube 3 cm length, 3 cm width, 3 cm heighti. 3 cm x 3 cm x 3 cm = 9 cm3

Liquid volume3. Can’t actually measure size of water but

measure the container it is in

4. Liquid volume units = liter (L) or milliliter (mL)

Measuring Time and TemperatureTime – interval between 2 events

1. SI unit – (s) seconds

Temperature – a measure of how hot or cold something is (thermal energy)

2. Celsius (oC)

– body temp – 37oC room temp – 20oC freezing point – 0oC boiling – 100oC

3. Kelvin (K) – 0 K is coldest possible temperature

freezing point – 273 K boils – 373 KoC = K – 273 K = oC + 273

Converting within the metric system

A. Although the basic units are sufficient for most measurements, many times it is necessary to talk about amounts so big, or so little that the numbers would be hard to understand if they were reported in m,g,or l.

Converting Within the Metric System

Conversion FactorA. Conversion factors (a ratio that is equal to

one) are used to change one unit to another1. Ex) 1000 mL in 1 L

2. 1000 mL = 1 1000 mL = 1L = 1

1 L 1L 1L

3. 1L = 1

1000 mL

kilogram (kg) --- gram (g) --- pound (lb) --- ounce (oz) --- meters (m) miles (mi) --- centimeters (cm) --- feet (ft) --- gallon (ga) --- liters (L)inch (in) --- second (s) --- minute (min) --- hour (hr) --- milliliter (mL)kilometer (km) --- day (day) --- fluid ounce (fl oz) 1 mile = 5,280 feet --- 1,600 meters = 1 mile --- 1 pound = 16 ounces1 kilogram = 2.2 pounds --- 1 inch = 2.54 centimeters --- 1 ounce = 28.35 grams1 gallon = 3.79 liters --- 128 fluid ounces = 1 gallon1,000 grams = 1 kilogram1,000 milliliters = 1 liter --- 1,000 meters = 1 kilometer

Understanding size in metric conversions

A. Which is larger 1m or 1cm?

B. Which is smaller 1km or 1dm?

Practice Converting Units

A. Convert 1m to cm.

A. How many grams are in 1.25 kg?

A. Convert 345.6 l to microliters.

Combining Skills

A. Which is bigger 1m or 100mm?

B. Which is smaller 3.25km of 3,250m?

Converting Using Dimensional Analysis

A. Many times it is necessary to convert from one unit to another using an equality:

1. Equationsa) Ex: Converting Celsius to Fahrenheit

2. Fractionala) Converting Metric to English

Examples

A. Convert 356.7 cm to inches

A. Convert 12.8m to inches

A. Convert 7 weeks into seconds