Answer in complete sentences. 1.What is the volume in this graduated cylinder (in mL)? 2.What is the uncertainty? 3.What could you do to find a more accurate value for the volume? 4.Do you think this graduated cylinder is accurate? Why or why not? 5.If I read volumes of 8.11, 8.12, and 8.10 mL from this picture, would my answer be accurate, precise, both, or neither? Explain your answer.
An engineer was responsible for calculating amount of water that overflowed from a dam. He measured all of the water runoff going into the reservoir (1.2 million cubic feet per year), the rainfall (860 cubic feet per year), and the capacity of the reservoir (3.8 million cubic feet). He did some fancy calculations. He reported to his boss that the overflow from the dam would be 350, cubic feet per year. What’s wrong here?
Significant Figures and Scientific Notation
I. Significant Figures aka: Significant Digits A. Nonzero integers count as significant figures –Ex. Any number that is NOT zero (1, 2, 3, 4, 5, 6, 7, 8, 9) –345 –597.2 –
Zeros –B. Leading zeros that come before all the nonzero digits do NOT count as significant figures –Ex: has two sig. fig. The zeros are “leading” and do not count. –0.23 – –
–C. Captive zeros are between nonzero digits and DO count as sig. fig. –Ex: has four sig. fig. The zeros are captive and DO count. –10,004 – –1,000,000,000,000,567
–D. Trailing zeros are to the right end of the number and DO count as sig. fig. if the number contains a decimal point. –Ex.: 100 has only one sig. fig. because the trailing zeros DO NOT have a decimal point. –Example: 1.00 has three sig. fig. because the trailing zeros DO have a decimal point. – –3,000,000 – –30.00 –300 –300.
E. Exact numbers –Any number found by counting has an infinite number of significant figures. –Ex: I have 3 apples. The 3 has an infinite number of significant figures. –50 people –100 baseballs
Which are exact numbers? 1.The elevation of Breckenridge, Colorado is 9600 feet. 2.There are 12 eggs in a dozen. 3.One yard is equal to meters. 4.The attendance at a football game was 52,806 people. 5.The budget deficit of the US government in 1990 was $269 billion. 6.The beaker held 25.6 mL of water.
Practice – Copy the number and identify the number of significant figures nine x10 32
How many significant figures? 1.A student’s extraction procedure yields g of caffeine. 2.A chemist records a mass of g in an analysis. 3.In an experiment, a span of time is determined to be x s. 4.Rewrite x so it has three significant figures.
The sample of gold contained 1,200,000,000,000,000,000,000,000,000 atoms. How do we keep track of ALL those zeros? In chemistry, some numbers are HUGE!
II. Scientific Notation (aka: Exponential Notation) 8,000,000 = = Integer must be 1≤x<10 Positive exponent: number > 1 Negative exponent: number 0!)
4,500,000 3,950,000,
Copy the number and rewrite in scientific notation a.100,000 b.-5,000,000 c.450,000,000,000 d.1,300 e.0.01 f g h
Remember… A negative exponent is a tiny number but is bigger than 0 (NOT a negative number!) A big exponent is a HUGE number. A negative number can have either a positive exponent or a negative exponent.
Round to three sig. fig. and express in exponential notation , ,321,
Homework Handout: Significant Figures and Scientific Notation
III. Rules for Sig. Fig. in Mathematical Operations A. Multiplication and Division –The number of sig. fig. in the results should be the same as the number of sig. fig. in the least precise measurement used in the calculation. –Example: 4.56 x 1.4 = 6.38 6.4
B. Addition and Subtraction –The result should have the same number of decimal places as the least precise measurement used in the calculation. –Example: = 31.1 (one decimal place)
13 x = = x 400 = 9380 = 5000 / 3.12 = …
= = – =
IV. Rounding Calculate first, then round Example: round to two sig. fig. –4.3 –Never round until your final answer!
Assignment P. 32 #8