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# 1.2 Measurements and Uncertainties PowerPoint PPT Presentation

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

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

• 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

• 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

• Ex. Length.

• Base unit is meter.

## Units and Standards

### 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

### 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 units.

• Others have special names

### 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

93,000,000 = 9.3000000

### Step 2

• Write the number without zeros

93,000,000 = 9.3

7

93,000,000 = 9.3 x 10

### Step 3

• Count how many places you moved decimal

• Make that your power of ten

The power of

ten is 7 because

the decimal

moved 7 places.

7

93,000,000 = 9.3 x 10

• 93,000,000 --- Standard Form

• 9.3 x 107 --- Scientific Notation

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

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

3) 9 x 1010

• 7.34 x 108

2)8.7 x 1011

### Complete Practice Problems

Write in scientific notation.

• 50,000

• 7,200,000

• 802,000,000,000

1) 5 x 104

2) 7.2 x 106

3) 8.02 x 1011

• 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

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

• 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

• 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

26.5 one decimal place

• 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

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) 10.47020D) 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