Math: The Central Language of Science



Math: The Central Language of Science

Physics - Chapter 2

Types of measurement

1 _________________________ - use numbers to describe

1 Easy to _______________________

2 Easy to ________________ upon, no personal bias

3 The measuring instrument limits how good the measurement is

2 _________________________ - use description without numbers

Measurements - Quantitative

1 Unit of measurement – the _____________________ being measured

2 Pure number – the __________________ of units determined by the act of measuring

3 ___________________ – the product of the pure number and the unit of measurement

Your Turn to Decide: Quantitative or Qualitative

1 4 feet

2 extra large

3 Hot

4 100 ºF

5 Sunny

6 96

Système International d’Unités

1 SI Units – the _______________ system

2 ______________ base units

1 mass, length, time, mol, temperature, electric current, luminous intensity

3 Many __________________ units

1 Density, volume

Base Units

1 Mass – ________________ (kg)

2 Length – meter (______)

3 ______________ – second (s)

4 Amount of substance – mole (___________)

5 Temperature – _________________ (K)

6 Electric Current – _________________ (A)

7 Luminous Intensity – __________________ (cd)

Derived Units

1 _______________ = mass ÷ volume

2 Volume = length • width • height

3 _________________ = Newton • length

4 Newton = mass • _________________

5 _________________ = length ÷ time squared

Dimensional Analysis

1 ________________________ from one unit to another

2 Conversion Factor – a ____________________ (ratio) comparing two units

1 Examples:

1 12 inches = 1 foot

2 3 feet = 1 yard

3 100 cm = 1 m

4 60 s = 1 min

3 Conversion factors can be __________________!!

Grid Method for Conversions

Grid Method for Conversions

Grid Method for Conversions

Dimensional Analysis

How good are the ___________________________________?

1 Scientists use two words to describe how good the measurements are

1 _____________________________- how close the measurement is to the actual value

2 _____________________________- how well can the measurement be repeated

Differences

1 Accuracy can be true of an ________________ measurement or the average of several

2 Precision requires ________________ measurements before anything can be said about it

In terms of measurement

1 Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across.

2 Were they precise? __________________

3 Were they accurate? __________________

The Metric System

1 An easy way to measure

17 Converting

k h D d c m

1 how far you have to move on this chart, tells you how far, and which direction to move the decimal place.

2 The box is the base unit, meters, Liters, grams, etc.

Significant figures (sig figs)

1 How many numbers mean anything

2 When we measure something, we always _______________ between the smallest marks.

3 The better marks the better we can estimate.

4 Scientist always understand that the last number measured is actually an estimate

Sig Figs

1 All _________________ numbers are ________________!

2 So….what do we do with zeros??

3 We follow the _________________!

Significant Digit Rules

1 Only applied to ____________________ data.

1 _____________________ numbers are infinitely significant!

2 All ________________ digits are _____________________!

3 All zeros ______________________ nonzero digits are significant!

4 In a ___________ number all zeros to the _______ of the last nonzero digit are significant!

5 In a decimal number all zeros to the _____ of the first nonzero digit are ______ significant!

6 In a number _________________ a decimal all trailing zeros (zeros to the right of the last nonzero digit) are _______________ significant!

Remember….

1 Scientific Notation only shows significant digits in the decimal part of the expression.

2 A decimal point following a zero at the end of the number indicates that the zero is significant.

Problems

1 50 has only 1 significant figure

1 if it should have two, how can I write it?

1 A __________________________ following a zero at the end.

2 ____________

2 A line over the significant zero

i) 50

3 Scientific notation

1 5.0 x 101

1 now the zero counts

How many sig figs in the following measurements?

5 458 g

6 4085 g

7 4850 g

8 0.0485 g

9 0.004085 g

10 40.004085 g

11 405.0 g

12 4050 g

13 0.450 g

14 4050.05 g

15 0.0500060 g

Rules for calculations with Significant Digits

23 Adding and Subtracting with Sig Figs

1 The last sig fig in a measurement is an _________________________.

2 Your answer when you add or subtract can not be better than your _________ estimate.

3 ___________ the answer to the least precise place of the measurement in the problem

Rounding rules

1 round 45.462 to four sig figs _________________

2 to three sig figs _____________________

3 to two sig figs _____________________

4 to one sig fig ______________________

Practice

1 4.8 + 6.8765

2 520 + 94.98

3 0.0045 + 2.113

4 6.0 x 102 - 3.8 x 103

5 5.4 - 3.28

6 6.7 - 0.542

7 500 -126

8 6.0 x 10-2 - 3.8 x 10-3

Multiplication and Division

1 Rule is simpler: Same number of sig figs in the answer as the one with the least number of sig figs in the question

2 3.6 x 653

1 2350.8

3 3.6 has 2 s.f. 653 has 3 s.f.; answer can only have 2 s.f.

4 2400

Practice

1 5.345 • 3.9

2 4.5 ÷ 6.245

3 4.50 • 6.245

4 9.8764 • 0.043

5 3.876 ÷ 1983

6 16047 ÷ 700

7 2400 • 123

8 4.5 x 102 • 1.45 x 103

What about angles and trigonometry

a) SI Unit is ___________________

b) Radian – the plane angle that subtends a circular arc equal to length to the radius of the circle

c) _____________ = _________________

d) Angles measured with a protractor should be reported to the nearest ________________

1) Conversions:

a) Report angles resulting from trig calculations to the ______________ precision of any angles given in problem

b) Assume trig ratios for angles given are pure numbers and do not take into account _____________

Instruments

30 Tools used to _________________

31 ______________ to modern scientific research

32 _____________________________

Error

34 The simple ______________ of the ___________________ and ___________________ values

35 May be __________ or __________

36 Absolute Error - _____________________ of the difference

Percentage Error

Problem Solving

40 Read CAREFULLY!

41 What information is _________________?

42 What information is _________________?

43 Make a ______________ _____________

44 Determie the method of _____________________

45 ________________ and _________________

46 Check your answer for ___________________

47 Does it have the expected __________________ and ______________?

48 Make a mental ________________

49 Be sure to simplify ________________

50 Express results to the correct number of ____________

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