Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Bra–ket notation wikipedia , lookup
Abuse of notation wikipedia , lookup
Approximations of π wikipedia , lookup
Large numbers wikipedia , lookup
Musical notation wikipedia , lookup
Big O notation wikipedia , lookup
History of mathematical notation wikipedia , lookup
Integrated Math Worksheet Name ______________________________ Period___________ Part 1 Rounding off When performing calculations, answers frequently come out uneven, with many decimal places. You will be expected to round off numbers to one or two decimal places, depending on the directions given and the measurements you have obtained. Generally, you will not use fractions in this course. 97.268 > 97.3 (1 place) Round off the following numbers to 139.428 > 139.43 (2 places) Round off the following numbers to the nearest tenth. the nearest hundredth. 1. 10.76 _________ 7. 10.768 2. 1369.07 _________ 8. 1369.074 ________ 3. 0.134 _________ 9. 0.134 ________ 4. 1.549 _________ 10. 1.549 ________ 5. 0.09 _________ 11. 0.096 ________ 6. 10.02 _________ 12. 2.349 ________ Part 2 Division ________ The mathematical procedure of division can be written many ways. For example, the problem of 4 divided by 5 can be written any of the following ways: A. 4÷5 B. 4 ∕ 5 C. 4 D. 5 4 5 When performing division on a calculator, the keystrokes should follow the method in example A above. Solve the following division problems rounding all answers to the nearest tenth. 13. 75 ∕ 107 14. 36÷7 15. 20 65 16. 10000 77000 Part 3 Solving equations The equation A = B/C consists of three variables. Given a value for any two of the variables, you should be able to solve for the value of the third. For example, if B = 6 and C = 2, then you would calculate A = 3. Or is A = 12 and C = 2, then you would calculate that B = 24. Solve the following problems using algebra rounding all answers to the nearest hundredth. 17. 9 = x-1 18. 7x = 35 19. -5 + x = 2 20. x / 4 = 4 21. 2 + x = 7 22. x – 7 = -7 23. x + 9 = 3 24. x – 9 = -9 25. x + 5 = 16 26. 5 + x =13 27. 6x + 7 = 61 28. -5x – 9 = -59 29. 3x + 4 = 7 30. 4x + 3 = 7 31. 4x – 2 = 26 32. -7x + 9 = -12 33. 3x + 5 = 14 34. -3x + 7 = 16 35. 2x + 8 = 12 36. 5 – 5x = -40 37. Velociraptors has a footprint length of 0.2 meters. Calculate the hip height using the equation hip height (H) = 4.5 x footprint length (FL) 38. Using the previous equation, a person measures their hip height as 0.85 meters, what it their footprint length? 39. A person has a footprint length of 0.23 meters, what is their hip height? Part 4 Rearranging equations Rearrange the following to solve for the different variables that are asked for. For example a x b = c can be rearranged to solve for both b and c. If solving for b, you would divide both sided by “a”, leaving you with b = c/a. If solving for a, you would divide both sides by “b”, leaving you with a = c/b. 40. gh=x, solve for h. 41. a – 5 = d, solve for a. 42. y + 9 = w, solve for y. 43. efg = h, solve for f. 44. v/d = m, solve for d. 45. v/d = m, solve for v. 46. ab/2=c, solve for a. Part 5 Density Objects have their own unique properties. Use the equation density(d)=mass(m)/volume(v). Remember volume for a rectangular object can be calculated by multiplying length times width times height. If you are finding the volume of an irregular object you a find it using a graduated cylinder by subtracting final volume minus initial volume. 47. Tell what the equation would look like if you are solving for the following variables. d= m= v= 48. A pine block is pictured below. The mass of the block is 11.31 grams. What is the density of this block? List the steps you would use the find the density and solve the problem showing the work. Make sure you use the correct units. 2.3 cm 3.6 cm 3.4 cm 49. The density of gold is 19.32 g/cm3. You have found a nugget and have calculated the mass at 39 grams and the volume of as 3.2 cm3. Is this nugget gold? How would you solve the problem? 50. Bromine is a reddish brown liquid. Calculate the density of Bromine that has a mass of 586 grams and it occupies 188 mL. (1 cm3 = 1 mL) Part 5 Scientific notation Scientific notation provides a place to hold the zeroes that come after a whole number or before a fraction. The number 100,000,000 for example, takes up a lot of room and takes time to write out, while 108 is much more efficient. Though we think of zero as having no value, zeroes can make a number much bigger or smaller. Think about the difference between 10 dollars and 100 dollars. Even one zero can make a big difference in the value of the number. In the same way, 0.1 (one-tenth) of the US military budget is much more than 0.01 (one-hundredth) of the budget. The small number to the right of the 10 in scientific notation is called the exponent. Note that a negative exponent indicates that the number is a fraction (less than one). The line below shows the equivalent values of decimal notation (the way we write numbers usually, like "1,000 dollars") and scientific notation (103 dollars). For numbers smaller than one, the fraction is given as well. smaller Fraction 1/1000 bigger 1/100 1/10 Decimal notation 0.001 0.01 0.1 1 10 100 1,000 ____________________________________________________________________________ Scientific notation 10-3 10-2 10-1 100 101 102 103 Practice with Scientific Notation Write out the decimal equivalent (regular form) of the following numbers that are in scientific notation. Section A: Model: 101 = 10 51) 102 = _______________ 54) 10-2 = _________________ 52) 104 = _______________ 55) 10-5 = _________________ 53) 107 = _______________ 56) 100 = __________________ Section B: Model: 2 x 102 = 200 57) 3 x 102 = _________________ 60) 6 x 10-3 = ________________ 58) 7 x 104 = _________________ 61) 900 x 10-2 = ______________ 59) 2.4 x 103 = _______________ 62) 4 x 10-6 = _________________ Section C: Now convert from decimal form into scientific notation. Model: 1,000 = 103 63) 10 = _____________________ 66) 0.1 = _____________________ 64) 100 = _____________________ 67) 0.0001 = __________________ 65) 100,000,000 = _______________ 68) 1 = _______________________ Section D: Model: 2,000 = 2 x 103 69) 400 = ____________________ 72) 0.005 = ____________________ 70) 60,000 = __________________ 73) 0.0034 = __________________ 71) 750,000 = _________________ 74) 0.06457 = _________________