1.2 measurements and uncertainties. 1.2.1 state the fundamental units in the si system in science,...

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


• 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.


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

Units and Standards

• Ex. Length.• Base unit is meter.

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)


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


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

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

1.2.3 Convert between different units of quantities

Convert your age into seconds.

Most people can do that if given a few minutes. But do you know what you were doing.

Write what you know.


Let’s break it down.

1. Write what you know.

2. The unit you are coming from goes on bottom.

3. The unit you are going to is placed on top.

4. Multiply on the top and bottom and simplify!


Let’s break it down.

a) 32ft = ______in

b) 100lbs = ______ kg

c) 85cm = _______ in

1.2.4 State unites in the accepted SI format1.2.5 State values in scientific notation and in

multiples of units with appropriate prefixes

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

93,000,000 miles

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

1.2.7 Distinguish between precision and accuracy

Accuracy is how close to the “correct” value

Precision is being able to repeatedly get the same value

Measurements are accurate if the systematic error is small

Measurements are precise if the random error is small.

Examples: groupings on 4 different targets

Example of precision and accuracyA voltmeter is being used to measure the potential difference across an electrical component. If the voltmeter is faulty in some way, such that it produces a widely scattered set of results when measuring the same potential difference, the meter would have low precision. If the meter had not been calibrated correctly and consistently measured 0.1V higher than the true reading (zero offset error), it would be in accurate.

1.2.6 Describe and give examples of random and systematic errors.

1.2.8 Explain how the effects of random errors may be reduced.

There are two types of error, random and systematic.

Random Errors - occur when you measure a quantity many times and get lots of slightly different readings.

Examples - misreading apparatus, Errors made with calculations, Errors made when copying collected raw data to the lab report

Can be reduced by repeating measurements many times.

Measurements are precise if the random error is small

1.2.6 Describe and give examples of random and systematic errors.

1.2.8 Explain how the effects of random errors may be reduced.

There are two types of error, random and systematic.

Systematic error – when there is something wrong with the measuring device or method

Examples – poor calibration, a consistently bad reaction time on the part of the recorder, parallax error

Can be reduced by repeating measurements using a different method, or different apparatus and comparing the results, or recalibrating a piece of apparatus

Measurements are accurate if the systematic error is small.

Graphs can be used to help us identify different types of error.

Low precision is represented by a wide spread of points around an expected value.

Low accuracy is represented by an unexpected intercept on the y-axis. Low accuracy gives rise to systematic errors.

Accurate or Precise?

1.2.9 Calculate quantities and results of calculations to the appropriate number of

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


significant figures

The number of sig figs should reflect the precision of the value of the input data.

If the precision of the measuring instrument is not known then as a general rule, give your answer to 3 sig figs.

Three Basic RulesNon-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

Example Video

4:45

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

Adding and Subtracting

Base your answer on which number column is lacking significance.

25

+ 1.34

26.34 Calculated Answer

26 Rounded answer based on sig figs

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


significant figures

Practice

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

1.2.9 Practice 13(Dickinson)

A meter rule was used to measure the length, height and thickness of a house brick and a digital balance was used to measure its mass. The following data were obtained.

Length = 20.5cm, height = 8.4cm, thickness 10.2cm, mass = 3217.94g

Calculate the density of the house brick and give your answer to an appropriate number of sig figs.

1.2.9 Practice 13(Dickinson)

Solution

Density = (mass/volume)

Density = (3217.94/1756.44)

Density = 1.8320808 g cm-3

Density = 1.8 g cm-3

1.2.10 State uncertainties as absolute, fractional and percentage uncertainties.

Random uncertainties(errors) due to the precision of a piece of apparatus can be represented in the form of an uncertainty range.

Experimental work requires individuals to judge and record the numerical uncertainty of recorded data and to propagate this to achieve a statement of uncertainty in the calculated results.


Rule of Thumb

Analogue instruments = +/- half of the limit of readingEx. Meter stick’s limit of reading is 1mm so

it’s uncertainty range is +/- 0.5mm

Digital instruments = +/- the limit of the reading Ex. Digital Stopwatch’s limit of reading is

0.01s so it’s uncertainty range is +/- 0.01s


We can express this uncertainty in one of three ways- using absolute, fractional, or percentage uncertainties Absolute uncertainties are constants associated

with a particular measuring device. (Ratio) Fractional uncertainty = absolute uncertainty

measurementPercentage uncertainties = fractional x 100%

Example

A meter rule measures a block of wood 28mm long.

Absolute = 28mm +/- 0.5mm

Fractional = 0.5mm = 28mm +/- 0.0179

28mm

Percentage = 0.0179 x 100% =

28mm +/- 1.79%


Random uncertainties(errors) due to the precision of a piece of apparatus can be represented in the form of an uncertainty range.

Experimental work requires individuals to judge and record the numerical uncertainty of recorded data and to propagate this to achieve a statement of uncertainty in the calculated results.

1.2 measurements and uncertainties. 1.2.1 state the fundamental units in the si system in science,...

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