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1.2 Measurements and Uncertainties

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1.2 Measurements and Uncertainties

- 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.

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

- 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

- Some derived units don’t have any special names

- Others have special names

- 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)

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

- A number between 1 and 10
- A power of 10
N x 10x

149,000,000km

- Move the decimal to the left
- Leave only one number in front of decimal

93,000,000 = 9.3000000

- Write the number without zeros

93,000,000 = 9.3

7

93,000,000 = 9.3 x 10

- 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

----->

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?

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

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

- 3.40000 --- move the decimal

--->

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

Move the decimal to the right.

- 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?

- Precision:
- How closely two or more measurements of the same quantity agree with one another.
- Think: Can the measurement be consistently reproduced?

- 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

- 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

- 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 ________

- 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

26.54 answer

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

- 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

- 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

- 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