1.2 Measurements and Uncertainties

1.2.1 State the fundamental units in the SI system

• In science, numbers aren’t just numbers. • They need a unit. We use standards for

this unit.• A standard is:

• a basis for comparison• a reference point against which other things

can be evaluated

• Ex. Meter, second, degree

1.2.1 State the fundamental units in the SI system

• The unit of a #, tells us what standard to use.

• Two most common system:• English system• Metric system

• The science world agreed to use the International System (SI)• Based upon the metric system.

1.2.1 State the fundamental units in the SI system

1.2.1 State the fundamental units in the SI system

• Conversions in the SI are easy because everything is based on powers of 10

Units and Standards

• Ex. Length.• Base unit is meter.

Common conversions

2.54 cm = 1 in 4 qt = 1 gallon

5280 ft = 1 mile 4 cups = 48 tsp

2000 lb = 1 ton

1 kg = 2.205 lb

1 lb = 453.6 g

1 lb = 16 oz

1 L = 1.06 qt

Scientific Notation

1.2.2 Distinguish between fundamental and derived units and give examples of derived units.

Some derived units don’t have any special names

Quantity Name Quantity Symbol

Unit Name Unit Symbol

Area A Square meter

Volume V Cubic meter

Acceleration a Meters per second squared

Density p Kilogram per cubic meter

1.2.2 Distinguish between fundamental and derived units and give examples of derived units.

Others have special names

Quantity Name Quantity Symbol

Special unit name Special unit Symbol

Frequency f Hz

Force F N

Energy/Work E, W J

Power P W

Electric Potential V V

1.2.2 Distinguish between fundamental and derived units and give examples of derived units.

A derived unit is a unit which can be defined in terms of two or more fundamental units.

For example speed(m/s) is a unit which has been derived from the fundamental units for distance(m) and time(s)

Scientific Notation

A short-hand way of writing large numbers without writing all of the zeros.

Scientific notation consists of two parts:

A number between 1 and 10

A power of 10

N x 10x

149,000,000km

Step 1

Move the decimal to the left

Leave only one number in front of decimal

Step 2

Write the number without zeros

Step 3

Count how many places you moved decimal

Make that your power of ten

The power often is 7 becausethe decimalmoved 7 places.

93,000,000 --- Standard Form

9.3 x 107 --- Scientific Notation

Practice Problem

1) 98,500,000 = 9.85 x 10?

2) 64,100,000,000 = 6.41 x 10?

3) 279,000,000 = 2.79 x 10?

4) 4,200,000 = 4.2 x 10?

Write in scientific notation. Decide the power of ten.

9.85 x 107

6.41 x 1010

2.79 x 108

4.2 x 106

More Practice Problems

1) 734,000,000 = ______ x 108

2) 870,000,000,000 = ______x 1011

3) 90,000,000,000 = _____ x 1010

On these, decide where the decimal will be moved.

1) 7.34 x 108 2) 8.7 x 1011 3) 9 x 1010

Complete Practice Problems

1) 50,000

2) 7,200,000

3) 802,000,000,000

Write in scientific notation.

1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

Scientific Notation to Standard Form

Move the decimal to the right

3.4 x 105 in scientific notation

340,000 in standard form

3.40000 --- move the decimal

Practice:Write in Standard Form

6.27 x 106

9.01 x 104

6,270,000

90,100

Accuracy, Precision and Significant Figures

Accuracy & Precision

Accuracy:     How close a measurement is to the true

value of the quantity that was measured.Think: How close to the real value is it?

Accuracy & Precision

Precision:    How closely two or more measurements

of the same quantity agree with one another.

Think: Can the measurement be consistently reproduced?

Significant Figures

The numbers reported in a measurement are limited by the measuring tool 

Significant figures in a measurement include the known digits plus one estimated digit

Three Basic Rules

Non-zero digits are always significant. 523.7 has ____ significant figures

Any zeros between two significant digits are significant. 23.07 has ____ significant figures

A final zero or trailing zeros if it has a decimal, ONLY, are significant. 3.200 has ____ significant figures 200 has ____ significant figures

Practice

How many sig. fig’s do the following numbers have? 38.15 cm _________ 5.6 ft ____________ 2001 min ________ 50.8 mm _________ 25,000 in ________ 200. yr __________ 0.008 mm ________ 0.0156 oz ________

Exact Numbers

Can be thought of as having an infinite number of significant figures

An exact number won’t limit the math.1. 12 items in a dozen 2. 12 inches in a foot 3. 60 seconds in a minute

Adding and Subtracting 

The answer has the same number of decimal places as the measurement with the fewest decimal places.   

  25.2 one decimal place

+ 1.34 two decimal places

26.54  answer

26.5 one decimal place

Practice:Adding and Subtracting 

In each calculation, round the answer to the correct number of significant figures.

A. 235.05 + 19.6 + 2.1 =          

1) 256.75  2) 256.8  3) 257    

B. 58.925 - 18.2 =          

1) 40.725  2) 40.73  3) 40.7  

Multiplying and Dividing

Round to so that you have the same number of significant figures as the measurement with the fewest significant figures. 

42 two sig figs

x 10.8 three sig figs

453.6  answer

450 two sig figs

Practice:Multiplying and

Dividing In each calculation, round the answer to the correct number of significant figures.

A. 2.19 X 4.2 =

1) 9    2) 9.2   3) 9.198 

B. 4.311 ÷ 0.07 =          

1) 61.58    2) 62   3) 60

Practice work

How many sig figs are in each number listed? A) 10.47020 D) 0.060 B) 1.4030 E) 90210 C) 1000 F) 0.03020

Calculate, giving the answer with the correct number of sig figs. 12.6 x 0.53 (12.6 x 0.53) – 4.59 (25.36 – 4.1) ÷ 2.317