Name CHM111 Lab Math Review Grading Rubric Part 1. Basic Algebra and Percentages Criteria Points possible Points earned Question 1 (0.25 points each question) 2 Question 2 (0.25 points each question) 1 Question (0.25 points each question) 1 Part II. Number of Sig figs (Question 4) (0.50 points each question) 4 Part III. Rounding and Sig figs in calculations Question 5 (0.50 points each question) 2 Question 6 (0.50 points each question) 2 Question 7 (0.50 points each question) 2 Part IV. Scientific notation (Q8) (0.50 points each question) Part V. Operations with exponents (Q9) (0.50 points each question) Total 20 Subject to other additional penalties as per the instructor
CHM 111 Math Review I. Basic Algebra and Percentages Q1. Solve for the unknown (y) in each of the following cases. Show your work. 25 = 10 5y 50 + y = 2 4y + 6 = 15
Q2. Express the following as percentages 1/4 1/15 2/16 1/ Q. Solve the following percent problems: What percent of 40 is 15? What is 60% of 65? 150 is 45% of what number? 1.4 is what percent of 7.7? II. Determining the Number of Significant Figures (S. F.) in a Number All scientific measurements and calculations contain some uncertainty. Scientists have developed rules so that the level of uncertainty can be clearly communicated to other scientists. The last digit of any reported measurement contains uncertainty. In scientific measurements, some zeros are significant and considered part of the measurement while other zeros are non-significant or place-holder zeros and are not considered part of the measurement. Certain numbers in science contain no uncertainty and are called exact numbers. Exact numbers are things that have been counted or numbers that are part of a definition. Since there is no uncertainty, they are considered to have infinite significant figures. Rules for Counting Significant Figures: Example # S. F. In decimal numbers, everything to the right of the first non-zero is significant 4 0.00020 cm 60.0 in In non- decimal numbers, everything to the left of the last non-zero is significant 705000 km
Counting numbers and numbers in definitions are exact. 28 students 12 in (= 1 ft) Q4. Determine the number of significant figures in the following measurements: 650 nm 2.00 cm 0.001500 Kg 0200 Km 12 eggs 0.05 ml 16.001 g 0.125 L III. Rounding for Significant Figures in Calculations Calculations sometimes have to be rounded to correctly reflect the uncertainty of the final answer. Different rounding rules apply for addition/subtraction and multiplication/division. Addition/Subtraction Round the answer to place (tens, ones, hundredths, etc.) with the most uncertainty in the numbers being added/subtracted. In the examples below, the uncertain digit in each number has been underlined. (Note: if numbers have exponents, the exponents must be the same for this rule to be applied.) 0.020 (uncertainty in thousandths place) 2400 (uncertainty in hundreds place) + 0.1256 (uncertainty in ten-thousandths place) + 542 (uncertainty in ones place) 0.1456 è 0.146 (rounded to thousandths place) 2942 è 2900 (rounded to hundreds place)
Q5. Perform the following calculations and round to the correct number of significant figures 14.22 + 2.6 = 11.001-6. + 2.66 = 71.6-21 + 10 = 2.2 x 10 +.24 x 10 2 = Multiplication/Division Round the answer to have the same number of significant figures as the number with the least number of significant figures. 5.60 ( sig figs) 2.00 x 10 8 (4 sig figs) x 0.022 (2 sig figs) 4 x 10-5 (1 sig fig) 0.122 0.12 (rounded to two sig figs) 5.75 x 10 12 6 x 10 12 (rounded to 1 sig fig) Q6. Perform the following calculations and round to the correct number of significant figures 1700 2.7 = 0.50 x 0.24 = 8.46 x 10 12 4.5 x 10 5 = 50 x 7.500 = Multiple Operations Apply the addition/subtraction and multiplication/division rules sequentially according to the order of operations. Underline the place where the significance ends after each operation and round at the last step. (8.456 8.12) = (0.6) (significance ends in the hundredths place = 2 sig figs) = 0.04179 8.12 8.12 ( sig figs) = 0.041
Q7. Perform the following calculations and round to the correct number of significant figures (5.610-5.52) 5.52 = 12.45 + (0.25 x 1.2) 2.56/.1 + 0.470/.062 = (9.5 + 4.1 + 2.6)/2.5 IV. Scientific Notation A number written in scientific notation has two parts: a coefficient which is a number between 1 and 10 and an exponent 10 raised to a power. For example, consider the number 1.2 10 2. Here 1.2 is the coefficient and 10 2 is the exponent. We can convert between regular and scientific notation by moving the decimal place either to the left or the right. For every place moved to the right, the power of 10 decreases by 1. For every decimal place moved to the left, the power of 10 increases by one. Place the decimal place after the first non-zero digit. Two examples are shown below. The decimal was moved places to the left and placed after the first non-zero digit 5 The decimal was moved 4 places to the right and placed after the first non-zero digit 2 Entering Scientific Notation on a Calculator. The most efficient way enter scientific notation on a calculator is to use the exponent button, usually labeled E or EE or exp on or above the button. On most calculators 1.5 x 10 - would be entered as 1.5E-. Try entering it this way on your calculator and press return. The display should read 0.0015. When converting to scientific notation, the number of significant figures should not change. 40.0 has significant figures; in scientific notation it would be 4.00 x 10 1 Q8. Convert the following to scientific or regular notation. The number of significant figures should be the same in both formats. Regular notation Scientific Notation Scientific Notation Regular notation 0.000451 1.574 x 10 18 050 000 2.0 x 10-20.20 9.51 x 10-6
V. Mathematical operations involving exponents You should be comfortable doing operations with exponents in your calculator. Use of the exponent button allows you to skip using parentheses. Enter the following in your calculator: 4.0 x 10 5 2.0 x 10 5 The answer should be 2. If you got 2 x 10 10, you need to use either parentheses or your exponent button. If you enter 4.0 x 10^5 /2.0 x 10^5, your calculator thinks you mean: 4.0 x 10 5 x 10 5 2.0 To get the correct answer you must enter either: 4.0 x 10^5 /(2.0 x 10^5) or 4.0E5/2.0E5 Note that using the exponent button saves time in reducing the number of key strokes Q9. Carry out the following calculations and report your answer in scientific notation with the correct number of significant figures. 6.5 x 10 2. x 10 7 = 6.022 x 10 2 2.89 = 4.2 x 10 4 8.75 x 10 1 = (6.66 x 10 4 2.0 x 10 8 ) 525 x 10-9 5.79 x 10 4 + 2.15 x 10 4 = 1.21 x 10 - + 0.215x 10-4 =