Chapter 3- lec 1: Find the length of a paperclip with each of the three “rulers” Ruler a Ruler b Ruler c Were all of your measurements identical 2. Which measurement are you most uncertain of (required the greatest amount of estimation)?

Uncertainty in measurement Measurements are only as precise as the instrument used. Uncertainties of measurements are predictable and can be calculated. They can be estimated to be half of the smallest division on a scale. The last # which you estimate is the uncertain number.

Write down the following measurements. Include uncertainties.

Precision and Accuracy Accurate- Measurements that are close to the “correct” value Precise- Measurements that are close to each other.

Measurements… actual= 2.4cm Student A Student B Trial 1 2.5 cm 1.8cm Trial 2 2.4 cm 1.7cm Trial 3 2.3 cm Average: 2.4cm 1.76cm Were either of the students accurate? Which one? WHY? 2. Were either of the students precise? Which one? WHY?

Percent error ·A way to explain the degree of error of a measurement. ·Uses the equation: Accepted value = actual, theoretical, true, known Example: Calculate the percent error of student B’s average

Units Notes Units: the scale that goes with numbers There are 3 systems: English – in America (ex. Foot, pound) Metric- EVERYWHERE (ex. Meter, gram) SI – for science Based on metric

The Fundamental SI base units measurement unit abbreviation instrument picture

The Fundamental SI base units measurement Length unit meter abbreviation m instrument ruler Picture

The Fundamental SI base units measurement Length mass unit meter kilogram abbreviation m kg instrument ruler Balance picture

The Fundamental SI base units measurement Length mass volume unit meter kilogram liter abbreviation m kg l instrument ruler Balance Graduated cylinder picture

The Fundamental SI base units measurement Length mass volume temperature unit meter kilogram liter Kelvin abbreviation m kg l K instrument ruler Balance Graduated cylinder thermometer picture

The Fundamental SI base units measurement Length mass volume temperature time unit meter kilogram liter Kelvin second abbreviation m kg l K s instrument ruler Balance Graduated cylinder thermometer stopwatch picture

Mass Mass = quantity of matter in an object. Weight= force exerted on an object by gravity. Which of these quantities does not change?

Exponents- Review 100 = 101 = 102 = 103 = 10-1 = 10-2 = 10-3 =

Exponents- Review 100 = 1 101 = 10 102 = 100 103 = 1000 10-1 = .1 10-2 = .01 10-3= .001

Scientific Notation (same as exponential notation) It looks like: N X 10M N is a number between 1 and 10 If M is positive it’s a # > 1 When M is negative it’s a # <1.

Ex. 1: The distance from the earth to the sun is 93,000,000 miles - Sci not = 9.3 X 107 Notice 9.3 is between 1 and 10. And the exponent 7 is positive, because it represents a value larger than 1.

Ex. 2 The diameter of an atom is 0.00000000562cm Scientific notation = 5.62x10-9 5.62 is between 1 and 10 The exponent is negative -9 because it represents a value smaller than 1.

Ex. 3: Convert 2.3 x 102 to standard notation. The decimal moves over 2 places to make the number larger (its positive) = 230

Ex. 4: Ex:4 convert 3.6 x 10-4 in to standard notation

Ex. 5: Convert 2.54 x 106 into standard notation

Try these 4 on your own… Convert 0.0000003 to scientific notation 3. convert 3.4 x 107 to standard notation 4. Convert 2 x 10-3 to standard notation

Multiplication Multiply the coefficients and add the exponents. (3 x 104) x (2 x 102) = (3 x 2) x 104+2 = 6 x 106 (2.1 x 103) x (4.0 x 10–7) = (2.1 x 4.0) x 103+(–7) = 8.4 x 10–4

Division Divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator. 3.0 x 105 3.0 = x 105–2 = 0.5 x 103 = 5.0 x 102 6.0 x 102 6.0

Addition and Subtraction If you are not using a calculator, then the exponents must be the same (the decimal points must be aligned). (5.4 x 103) + (8.0 x 102) = (5.4 x 103) + (0.80 x 103) = (5.4 + 0.80) x 103 = 6.2 x 103

Practice problems Solve each problem and express the answer in scientific notation. a. (8.0 x 10–2) x (7.0 x 10–5) b. (7.1 x 10–2) + (5 x 10–3)

Practice problems Solve each problem and express the answer in scientific notation. a. (8.0 x 10–2) x (7.0 x 10–5) = 5.6 x 10–6 b. (7.1 x 10–2) + (5 x 10–3) = 7.6 x 10–2