chapter 2 – section 2 suggested reading pages 33-42 units of measurement

Chapter 2 – Section 2

Suggested Reading

Pages 33-42

Units of Measurement

Making Measurements

Measurements must have a number and a unit.

The unit depends on the quantity being measured.

SI Measurement

Le Systeme International d’Unites

See Table of SI Base units – Page 34

See Table of SI Prefixes – Page 35

Standard SI Units

Length = meter (m)

Mass = kilogram (kg)

Time = second (s)

Temperature = Kelvin (K)

Amount of substance = mole (mol)

Derived SI Units

Area = square meter (m2)

Volume = cubic meter (m3)

Density = kilograms per cubic meter (kg/m3)

Produced by multiplying or dividing standard units.

Definitions

Mass – a measure of the quantity of matter in an object.

Weight – a measure of the gravitational pull on matter.

Volume – the amount of space occupied by an object.

Density – the ratio of mass to volume

The density of an object is calculated by

dividing the mass of the object by its volume.

Density

The object with the lowest density will float.

Density is a Derived Unit

Combination of base units

Mass (g or kg)

Volume (m3 or cm3) length length length

D = MV

1 cm3 = 1 mL1 dm3 = 1 L

Density (kg/m3 or g/cm3 or g/mL)

mass per volume

DensityM

ass

(g)

Volume (cm3)

Δx

Δyslope D

V

M

Density

An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass.

GIVEN:

V = 825 cm3

D = 13.6 g/cm3

M = ?

WORK:

M = DV

M = (13.6 g/cm3)(825cm3)

M = 11,200 g

V

MD We will talk about

how to round correctly soon!

Density

A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid?

GIVEN:

D = 0.87 g/mL

V = ?

M = 25 g

WORK:

V = M D

V = 25 g

0.87 g/mL

V = 29 mLV

MD

Dimensional Analysis –

The technique of converting between units.

Six Steps that May Help You:

1. Write down the starting number with unit, draw a horizontal line under it, and a vertical line next to it.

2. Look at the unit and write down conversion factors that might work. (You have to THINK of these.)

3. Write down UNITS for conversion factors ABOVE & BELOW the line so the unit you started with will CANCEL OUT.

4. Fill in the numbers that go with the conversion factors.

6. Do the math & don’t forget to round correctly at the end & put the correct unit on your final answer.

5. Cancel out units as required.

Example:

1. Write it down, draw the lines.

14 cm

Convert 14 cm to meters

Example:

14 cm

Convert 14 cm to meters

2. Write down the factor.

Our factor that we think will work is 100 cm = 1 meter

Example:

14 cm

Convert 14 cm to meters

Conversion Factor: 100 cm = 1 meter

3. Fill in the units from the factor so that the starting unit will cancel out.

cm

m

Example:

14 cm

Convert 14 cm to meters

Conversion Factor: 100 cm = 1 meter

cm

m

4. Fill in the numbers from the conversion factor.

100

1

Example:

14 cm

Convert 14 cm to meters

Conversion Factor: 100 cm = 1 meter

cm

m

100

1

5. Cancel out units.

Example:

14 cm

Convert 14 cm to meters

cm

m

100

1

6. Do the math.

Multiply all numbers across the top, divide by each number across the bottom.

= 14 100

= 0.14 mDon’t forgetunits!

1x

Example: Convert 4.7 kg to pounds

Some Problems Require Many Steps …Just draw a longer line!

Example:

1. Write it down, draw the lines.

4.7 kg

Convert 4.7 kg to pounds

Example:

4.7 kg

2. Write down the factors.

Our factors that we think will work are 454 g = 1 lb 1000g = 1 kg

Convert 4.7 kg to pounds

Example:

4.7 kg

Conversion Factors: 454 g = 1 lb and 1000g = 1 kg

3. Fill in the units from the factors so that the starting unit will cancel out.

kg

g

Convert 4.7 kg to pounds

g

lb

Example:

4.7 kg

4. Fill in the numbers from the conversion factors.

1

1000

Convert 4.7 kg to pounds

Conversion Factors: 454 g = 1 lb and 1000g = 1 kg

g

kg

lb

g

1

454

Example:

4.7 kg

1

1000

Convert 4.7 kg to pounds

Conversion Factors: 454 g = 1 lb and 1000g = 1 kg

g

kg

lb

g

1

454

5. Cancel out units.

*Example:

4.7 kg

1

1000

Convert 4.7 kg to pounds

g

kg

lb

g

1

454

6. Do the math.

Multiply all numbers across the top, divide by each number across the bottom.

=

=

Don’t forgetunits!

10. lb4.7 x 1000 x 1 1 454

How to measure

Mass – balance

Weight – a spring scale

Volume – volumetric flask