Chapter 2

Mathematics in Physics

Metric System

•A system of Measurements that

is based on the power of ten or multiples of ten

SI

International

System

•The system of measurements that has

been adopted by the scientific world based on the metric system

Basic Units

• Length meter m

• Mass kilogram kg

• Time second s

• Temp. kelvin K

• Matter mole mol

• Current amp A

• Lum. Int. candela cd

SI Prefixes

• Nano n 0.000000001 10-9

• micro 0.000001 10-6

• milli m 0.001 10-3

• centi c 0.01 10-2

• deci d 0.1 10-1

• kilok 1000 103

• mega M 1,000,000 106

• giga G 1,000,000,000 109

Scientific Notation

M x 10n

•1.00... M < 10

•n = an integer

M x 10n

•M is the coefficient

•n is the exponent

Convert each of the following to scientific

notation:620,000,000

0.000 000 000 045210,000

Addition & Subtraction in

Scientific Notation

• When adding w/o calculator– change all additives to the same power of

ten

– add coefficients

– power of ten remains constant

– 3 x 104 + 4 x 105 0.3 x 105 + 4 x 105

• When adding with calculator– all scientific notations must be within

parentheses

– 3 x 104 + 4 x 105 (3 x 104) + (4 x 105)

• When subtracting w/o a calculator–change all numbers to the same

exponent

–subtract coefficients

–keep exponents constant

• When subtracting with a calculator–place all scientific notations within

parentheses

Add:

4.10 x 1016 3.4 x 10-186

5.2 x 1015 6.20 x 10-185

Subtract:

4.10 x 1016 3.4 x 10-186

5.2 x 1015 6.20 x 10-185

Add: Subtract:

2.25 x 1016 3.40 x 10-18

7.7 x 1015 - 6.2 x 10-19

Multiplication & Division in Scientific Notation

• When multiplying w/o a calculator–multiply coefficients

–add exponents

• When multiplying with a calculator–place all scientific notations within

parentheses

• When dividing in w/o a calculator–divide coefficients

–subtract exponents

• When dividing in with a calculator–place all scientific notations within

parentheses

Multiply:

4.10 x 10126 2.0 x 10-186

3.0 x 1015 1.20 x 1018

divide:

4.40 x 1016 6.4 x 10186

2.2 x 1015 3.20 x 10-185

Compute:

4.40 x 10-6 6.4 x 10186

2.0 x 1015 3.20 x 1085x

Measurement Uncertainties

Accuracy

•How close the measurement is to

the correct measurement

Precision

•How well one can repeat the same

results in a measurement

Significant Digits

•The valid digits in a measurement

removing all digits that have too much uncertainty to count

Determine Sig Dig:• 215 21.5

• 21500 21.500

• 0.000 215 205

• 0.000 215 000 000

Conversion Factors

Ratios = 1

1 m

100 cm= 1

100 cm

1 m= 1

Conversion Factors• When you multiply any

number by a conversion factor, the number’s magnitude does not change

1 m

10-6 m= 1

1 nm

10-9 m= 1

1 cm

10-2 m= 1

1mm

10-3 m= 1

1 m

106 m= 1

1km

103 m= 1

109 m

1 Gm= 1

1Gm

109 m= 1

1 mm

10-3 m44 m x =

44 x 103 mm = 4.4 x 104 mm

Drill: Convert:1) 53 m to km2) 80 Gbytes to Mbytes3) 44 mg to ng

4) 62 cm to km

Parallax

•Differences in a measurement due

to the angle of observation

Common Units

•m = mass in (kg)

• t = time in (s)

•d = displacement in (m)

Common Units

•v = velocity in (m/s)

•a = acceleration in (m/s2)

•F = force in (N)

•N = Newton = kgm/s2

Common Units

•W = work in (J)

•J = Joules = kgm2/s2

•P = Power in (W)

•W = Watts = kgm2/s3

Graphing Data

Convert:1) 44 mm to km2) 21 s to Ms3) 64 cg to ng

Convert:1) 3.5 mm3 to m3

2) 3.6 km/hr to m/s

Density•A measure of mass

per unit volume

Density (D) ()

= m/V

Calculate the density of 750 g of a substance

occupying 12.5 mL of space.

Convert: 1) 23 cm/ms to km/ns 2) 56 g/nL to kg/ML

Convert:1800 km/hrto mm/ns

Convert: 47 g/nL to mg/L

Calculate the density in g/cm3 of a 0.62 Mg chunk

of metal that has dimensions of 12.5 mm by

4.0 m by 2.0 x 10-3 km.V = lwh = m/V

Convert: 144 km/hrto m/ns

Convert: 250 kg/m3 to

mg/cm3

Convert: 1)1800 miles/hr

to mm/ns2.54 cm = 1 inch

Drill: Convert:

4.6 g/nL to Mg/m3

1 mL = 1 cm3

Convert:2.5

xmiles/yearto m/ms

2.54 cm = 1.00 inch

Name & describe the seven basic

units

Name & give the multiple for: k, m,

M, , n, c, & G

Calculate the density in g/mL of 7.520 x 104 kg of

stuff occupying 2.5 x 103 m3 of space.

Calculate the volume in kL of an rectangular

prism with a length of 25 cm, width of 40.0 mm, & a height of

33500 mm.

Review LabDue

Monday