1 2 measurements and uncertainties
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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

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1.2 Measurements and Uncertainties

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1 2 measurements and uncertainties

1.2 Measurements and Uncertainties


1 2 1 state the fundamental units in the si system

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 system1

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 system2

1.2.1 State the fundamental units in the SI system


1 2 1 state the fundamental units in the si system3

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

1.2.1 State the fundamental units in the SI system


Units and standards

  • Ex. Length.

  • Base unit is meter.

Units and Standards


Common conversions

Common conversions

  • 2.54 cm = 1 in4 qt = 1 gallon

  • 5280 ft = 1 mile4 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

Scientific Notation


1 2 2 distinguish between fundamental and derived units and give examples of derived units

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

  • Some derived units don’t have any special names


1 2 2 distinguish between fundamental and derived units and give examples of derived units1

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

  • Others have special names


1 2 2 distinguish between fundamental and derived units and give examples of derived units2

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 notation1

Scientific Notation

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


Scientific notation consists of two parts

Scientific notation consists of two parts:

  • A number between 1 and 10

  • A power of 10

    N x 10x


The distance from the sun to the earth

The Distance From the Sun to the Earth

149,000,000km


Step 1

Step 1

  • Move the decimal to the left

  • Leave only one number in front of decimal

93,000,000 = 9.3000000


Step 2

Step 2

  • Write the number without zeros

93,000,000 = 9.3


Step 3

7

93,000,000 = 9.3 x 10

Step 3

  • Count how many places you moved decimal

  • Make that your power of ten


1 2 measurements and uncertainties

The power of

ten is 7 because

the decimal

moved 7 places.

7

93,000,000 = 9.3 x 10


1 2 measurements and uncertainties

  • 93,000,000 --- Standard Form

  • 9.3 x 107 --- Scientific Notation


Practice problem

9.85 x 107

----->

6.41 x 1010

----->

2.79 x 108

----->

4.2 x 106

----->

Practice Problem

Write in scientific notation.

Decide the power of ten.

  • 98,500,000 = 9.85 x 10?

  • 64,100,000,000 = 6.41 x 10?

  • 279,000,000 = 2.79 x 10?

  • 4,200,000 = 4.2 x 10?


More practice problems

More Practice Problems

On these, decide where the decimal will be moved.

  • 734,000,000 = ______ x 108

  • 870,000,000,000 = ______x 1011

  • 90,000,000,000 = _____ x 1010

Answers

3) 9 x 1010

  • 7.34 x 108

2)8.7 x 1011


Complete practice problems

Complete Practice Problems

Write in scientific notation.

  • 50,000

  • 7,200,000

  • 802,000,000,000

Answers

1) 5 x 104

2) 7.2 x 106

3) 8.02 x 1011


Scientific notation to standard form

  • 3.40000 --- move the decimal

--->

Scientific Notation to Standard Form

Move the decimal to the right

  • 3.4 x 105 in scientific notation

  • 340,000 in standard form


Practice write in standard form

6.27 x 106

9.01 x 104

6,270,000

90,100

Practice:Write in Standard Form

Move the decimal to the right.


Accuracy precision and significant figures

Accuracy, Precision and Significant Figures


Accuracy precision

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 precision1

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

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

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

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

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

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

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

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

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

Practice work

  • How many sig figs are in each number listed?

    • A) 10.47020D) 0.060

    • B) 1.4030E) 90210

    • C) 1000F) 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


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