PHYSICS Chapter 1 Review Rounding Scientific Notation Factor Label Conversions
The Tools Of PHYSICS
Metric Prefixes Prefix Symbol Meaning Kilo K 1000 Deci d tenth Centi c hundreth Milli m thousandth
Prefix Prefixes Used with SI Units Prefix Symbol Number Word Exponential Notation tera T 1,000,000,000,000 trillion 10 12 giga G 1,000,000,000 billion 10 9 mega M 1,000,000 million 10 6 kilo k 1,000 thousand 10 3 hecto h 100 hundred 10 2 deka da 10 ten 10 1 ----- ---- 1 one 10 0 deci d 0.1 tenth 10-1 centi c 0.01 hundredth 10-2 milli m 0.001 thousandth 10-3 micro µ 0.000001 millionth 10-6 nano n 0.000000001 billionth 10-9 pico p 0.000000000001 trillionth 10-12 femto f 0.000000000000001 quadrillionth 10-15
Rounding.64 Rounds down to.6.4 or less rounds down.
.66 Rounds up to.7.6 or more rounds up.
.65 Rounds down to.6 Even number followed by a 5 keep it even.
.55 Rounds up to.6 Odd number followed by a 5 round up to even.
Why this rounding method? Half the time the number in front of the 5 will be even and rounded down. Half the time the number following the 5 will be odd and rounded up. The error caused by rounding should be balanced out.
Scientific Notation Used for very large and very small numbers. Regular numbers are expressed as a number greater than 1 but less than 10, multiplied by a power of 10.
M x 10 n where 1 M < 10 and n = any integer n indicates which direction and how many spots to move the decimal point.
+n indicates that the original number is greater than one. -n indicates that the original number is less than one.
Scientific Notation Examples: 1234 1.234 x 10 + 3.0013-3 1.3 x 10 Original number > 1 Positive exponent Original number < 1 Negative exponent
6.02 x 10 2 + exponent Original number is > 1 Therefore: 602
6.02 x 10-2 - exponent Original number is < 1 Therefore: Zeros can be added to fill decimal spots..0602 Practice Numbers in SN.
Scientific Notation on the Calculator Discuss the scientific notation options on personal calculators and do sample calculator problems. Practice SN problems.
Precision and Accuracy When making measurements in the laboratory you need to know how good is the measurement. Precision indicates degree of reproducibility of a measured number.
Accuracy indicates how close your measurements are to the true value.
Precision and Accuracy in the Lab Precise and Accurate Precise but not Accurate
Not accurate but precise Accurate but low precision
Accuracy and Precision
P a r a l l a x
Measurements and Uncertainty It is not possible to know the exact measurement of anything. There is always going to be some guess work involved when measuring.
Beaker 47 ml Uncertain Digit
Significant Digits These are a PAIN!!! The greater the number of significant digits in a measurement, the greater the certainty.
1 cm 2 cm 1.6 cm
1.35 cm 1 cm 2 cm
1.72 cm 1 cm 2 cm
1.60 cm 1 cm 2 cm
2.00 cm 1 cm 2 cm
1. All nonzero digits are significant. 2. For numbers larger than 1 (one) that contain zeros. A. Zeros to the left of an UNDERSTOOD decimal point are NOT significant. 2300 contains 2 sig. figs.
B. Zeros to the left of an EXPRESSED decimal point ARE significant. 2300. Contains 4 sig. figs. 3. Zeros between nonzero digits are significant 2002 2.002 20.02 200.2 all have four sig.figs.
4. For numbers smaller than 1 (one) that contain zeros: A. Zeros to the right of a decimal but to the left of a nonzero digit are NOT significant. 0.0045 has two sig. figs.
B. Zeros to the right of a decimal and to the right of a nonzero digit ARE significant. 0.004500 has four significant digits. Exactness zeros
5. Exact numbers or definitions- numbers with no uncertainty. These have as many significant digits as the calculation requires. 60 min = 1 hr 1000 mg = 1 g Typically factor label conversions.
Math Operations and Sig. Figs. 1. Multiplication and Division The number with the least certainty limits the certainty of the result.
The answer can only have as many sig. figs as contained in the number with the least number of sig. figs. EX: 23000 X 1267 = 29,141,000 = 29,000,000
9.2 cm x 6.8 cm x 0.3744 cm = 23.4225 cm 3 or 23 cm 3
2. Addition and Subtraction The answer should be as accurate as the number with the lesser accuracy.
Adding two numbers: 23400 (+/- 100) + 230 (+/- 10) 23630 = 23600 +/- 100 Subtracting two volumes: 865.9 ml - 2.8121 ml 863.0879 ml = 863.1 ml +/- 0.1 ml
Measurements and Uncertainty It is not possible to know the exact measurement of anything. There is always going to be some guess work involved when measuring.
When Measuring Anything: Determine what the markings on the equipment mean. These are the certain digits.
Doubtful Digits in Measurements With any analog scientific tool the measurement can only be estimated to one spot past the certain digit. This estimated digit is also called the doubtful digit and is significant!!!
Factor Label Method of Conversions Utilizes comparisons of units to solve a problem.
Simple Examples of Factor Label 10 students attend a concert and pay $5 for a ticket. What is the total cost? 10 tickets x $ 5.00 = $50.00 ticket
If you baby sit for 3 hours and earn $4 per hour, how much do you earn? 3 hours x $ 4.00 = $12.00 hour
If you baby sit for 225 minutes and earn $4 per hour, how much do you earn? 225 min X 1 hour x 60 min $ 4.00 hour = $15.00
More Factor Label Convert 175 inches to feet. 175 in x 1 foot = 14.6 feet 12 in
Convert 25.0 cm to feet. Cm ---> inches ---> feet 25.0 cm x 1 inch x 2.54 cm 1 foot = 12 inches 0.82_ feet
Convert 25.0 gal to milliliters. Gallons ---> liters ---> ml 25.0 gal x 3.8 liters x 1 gal 1000 ml = 1 liter 95000 ml 9.50 x 10 4 ml
Convert 48 oz to kilograms. oz ---> lbs ---> grams ---> kg 48 oz x 1 lb x 16 oz 454 g x 1 lb 1 kg = 1.36 kg 1.4 kg 1000 g
How many seconds have you been alive? years ---> days ---> hours ---> sec 17 yrs x 365 days x 1 yr 24 hrs x 1 day 3600 sec = 5.36 x 10 8 sec 1 hr 5.4 x 10 8 sec
Area and Volume Factor Label Area conversions: How many cans of paint for a room? How much fabric? How many gallons of driveway sealer?
Convert 125 ft 2 to in 2. 2 125 ft x ( 12 in ) 2 = 18000 in 2 ( ) 2 1.80 x 10 4 in 2 1 ft The squares goes with the number and the unit.
Convert 1250 cm 3 to ft 3. 3 1250 cm x ( 1 in ) 3 x ( 2.54 cm ) 3 ( 1 ft ) 3 = ( 12 in) 3 0.0441 ft 3 The cubes goes with the number and the unit. 0.0441 ft 3
Graphing Data ch1_3_movanim.swf
Scatter plots of data may take many different shapes, suggesting different relationships.
H e i g h t o f P l a n t Age of Plant
Linear Relationships When the line of best fit is a straight line, the dependent variable varies linearly with the independent variable. This relationship between the two variables is called a linear relationship.
The relationship can be written as an equation. Y = mx +b
The slope is the ratio of the vertical change to the horizontal change. X 2,Y 2 X 1,Y 1
What is the slope of the graph? A.0.25 m/s 2 B.0.4 m/s 2 C.2.5 m/s 2 D.4.0 m/s 2
Nonlinear Relationships When the graph is not a straight line, it means that the relationship between the dependent variable and the independent variable is not linear. There are many types of nonlinear relationships in science. Two of the most common are the quadratic and inverse relationships.
The graph shown in the figure is a quadratic relationship. A quadratic relationship exists when one variable depends on the square of another.
A quadratic relationship can be represented by the following equation: y = ax2 + bx + c
The graph in the figure shows how the current in an electric circuit varies as the resistance is increased. This is an example of an inverse relationship.
P V Boyle s Law
In an inverse relationship, a hyperbola results. An inverse relationship can be represented by the following equation: y = a x
What is line of best fit? A.The line joining the first and last data points in a graph. B. The line joining the two center-most data points in a graph. C.The line drawn close to all data points as possible. D.The line joining the maximum data points in a graph.
Answer: C Reason: The line drawn closer to all data points as possible, is called a line of best fit. The line of best fit is a better model for predictions than any one or two points that help to determine the line.
Which relationship can be written as y = mx? A.Linear relationship B.Quadratic relationship C.Parabolic relationship D.Inverse relationship
Answer: A Reason: Linear relationship is written as y = mx + b, where b is the y intercept. If y-intercept is zero, the above equation can be rewritten as y = mx.
Which type of relationship is shown following graph? A. Linear B. Inverse C. Parabolic D. Quadratic
Answer: B Reason: In an inverse relationship a hyperbola results when one variable depends on the inverse of the other.
The End