Lab 1: Measurement. PART 1: Exponential Notation: Powers of 10

Transcription

1 Lab 1: Measurement Equipment: 2 meter sticks You will find these websites useful for today s lab: SI Base Units: Metric prefixes: PART 1: Exponential Notation: Powers of 10 Scientists look at things in very particular ways using sophisticated equipment, everyday instruments, and unlikely tools. Some things that scientists want to see are so small that they need a magnifying glass or a microscope. Other things are so far way and faint that they need a powerful telescope in order to see them. It is important to understand and be able to compare the size of things we are studying. Exponential notation is a way scientists write very large or very small numbers. For example, when the Earth is said to be meters wide, this number represents 1,000,000 meters. When a nucleus of a cell is seen at 10-6 meters wide, this number represents one millionth of a meter, or meters. Notice how each picture in this simulation is an image of something that is 10 times bigger or smaller than the one before or after it. The number on the right is the size of what is seen in the picture. The number on the left is the same number written in powers of ten, or exponential notation. In this simulation you will first view the Milky Way at 10 million light years from the Earth. Then move through space towards the Earth in single order of magnitudes until you reach an oak tree just outside the National High Magnetic Field Laboratory in Tallahassee, Florida. Then begin to move from the actual size of a leaf into the microscopic world through leaf cell walls, cell nucleus, DNA and finally, into the subatomic universe of electrons and protons. You will then manually reverse the direction, moving from smallest to largest value, as you log your powers-of-ten journey. Activity: Go to this website: Log your "Power of Ten" journey into the universe by completing this table describing your journey. Hopefully, you will be able to appreciate the powers of ten used in exponential notation and learn a few metric prefixes along the way. Watch the animation all the way through then you can step through it to fill out the following table (copy it into your lab report). Start small and manually move to the larger exponential values. Have a safe journey!

2 Power of Ten Description Location fermi Face to Face with a single Proton

3 What is the correct metric prefix for these powers of ten? a) b) 10-9 c) 10-6 d) 10-3 e) 10 3 f) 10 6 g) 10 9 h) i) How many times greater is the largest value compared to the smallest value in this Power of Ten Simulation? (Hint: Divide to find the ratio)

4 PART 2: MEASURING WITH SHADOWS Go outside with two meter sticks and measure the height of a building on campus. Here is how you can do it: Record the following in your lab report: Building Name Length of Ruler Shadow Length of Building Shadow Height of Building (meters) PART 3: MEASUREMENT & SIGNIFICANT FIGURES Read the following worksheet on significant figures, and do the practice problems. Then go to this website and do at least 10 drills per person (you do not have to write down the answers to your drills). Now, let s return to your results from Part 2. First, estimate the uncertainty in your measurement of the ruler s shadow and your measurement of the building s shadow. Think about a few things: what are the smallest tick marks on your ruler? How carefully did you measure each shadow? How certain is your group that the meter stick was really upright and not at an angle? Was the ground completely level? Rewrite your measurements in the following format. For example, let s say your shadow measurement was meters, and you think you could be off by 1 centimeter; your result would be / m. Length of Ruler Shadow +/- Uncertainty Length of Building Shadow +/- Uncertainty Explain with a few sentences why your group chose the uncertainty that you did for each of these measurements. Your uncertainty in each of these numbers determines the least significant digit in each of these numbers. Recalling the rules for significant figures, write a few sentences answering the following: How precisely do you know the height of the building that you measured? What could you have done differently in your measurement, or what extra equipment could you have used that would have increased your precision or reduced your uncertainty? Lab Credit: Adapted from Lynda Williams and Dr. Michael Carney

5 Rules for Significant Figures (sig figs, s.f.) A. Read from the left and start counting sig figs when you encounter the first non-zero digit 1. All non zero numbers are significant (meaning they count as sig figs) 613 has three sig figs has six sig figs 2. Zeros located between non-zero digits are significant (they count) 5004 has four sig figs 602 has three sig figs has 16 sig figs! 3. Trailing zeros (those at the end) are significant only if the number contains a decimal point; otherwise they are insignificant (they don t count) has four sig figs has six sig figs has two sig figs unless you re given additional information in the problem 4. Zeros to left of the first nonzero digit are insignificant (they don t count); they are only placeholders! has three sig figs has two sig figs also has two sig figs! B. Rules for addition/subtraction problems Your calculated value cannot be more precise than the least precise quantity used in the calculation. The least precise quantity has the fewest digits to the right of the decimal point. Your calculated value will have the same number of digits to the right of the decimal point as that of the least precise quantity. In practice, find the quantity with the fewest digits to the right of the decimal point. In the example below, this would be 11.1 (this is the least precise quantity) = (this is what your calculator spits out) In this case, your final answer is limited to one sig fig to the right of the decimal or 25.3 (rounded up). C. Rules for multiplication/division problems The number of sig figs in the final calculated value will be the same as that of the quantity with the fewest number of sig figs used in the calculation. In practice, find the quantity with the fewest number of sig figs. In the example below, the quantity with the fewest number of sig figs is 27.2 (three sig figs). Your final answer is therefore limited to three sig figs. (27.2 x 15.63) = (this is what you calculator spits out) In this case, since your final answer it limited to three sig figs, the answer is 230. (rounded down) D. Rules for combined addition/subtraction and multiplication/division problems First apply the rules for addition/subtraction (determine the number of sig figs for that step), then apply the rules for multiplication/division. E. Practice Problems 1. Provide the number of sig figs in each of the following numbers: (a) g (c) g (e) g (b) 3.40 x 10 3 ml (d) L (f) 1020 L 2. Perform the operation and report the answer with the correct number of sig figs. (a) (10.3) x ( ) = (c) [(10.3) + ( )] [(10.3) x ( )] (b) (10.3) + ( ) =