Scientific Notation Practice Quiz Put the following in
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Scientific Notation
Practice Quiz Put the following in order from smallest to largest. • 1. 8 x 10 -5 • 8. 7 x 1024 • 0. 7 x 10 -3 • 1. 4 x 1040
Answers Smallest 1. 8 x 10 -5 0. 7 x 10 -3 8. 7 x 1024 Largest 1. 4 x 1040
Scientists (and those studying science) frequently must deal with numbers that are very large or very small.
Instead of wasting time by writing many zeros before and after numbers, a method of writing very large and very small numbers was invented. It is called scientific notation.
1) The first figure is a number Rules from 1 to 9. 2) The first figure is followed by a decimal point and then the rest of the figures. 3) Then multiply by the appropriate power of 10.
Are these numbers written in scientific notation? • 60. 5 x 105 • 6. 05 x 106 -2 • 0. 65 x 10 2 • 4. 25
Examples • 425=4. 25 x 102 (102 is the same as 100, so you are really multiplying 4. 25 by 100) • 0. 00098=9. 8 x 10 -4 (10 -4 is the same as 1/1000, so you are really multiplying 9. 8 by 1/1000)
Practice Write the following in scientific notation: • 36000 • 0. 0135 • 3951 • 0. 632 • 0. 00000090
Answers • 3. 6 x 104 • 1. 35 x 10 -2 3 • 3. 951 x 10 -1 • 6. 32 x 10 -7 • 9. 0 x 10
Math is easy-use your calculator!!! • 4. 2 x 104 kg + 7. 9 x 103 kg= • 5. 23 x 106 mm x 7. 1 x 10 -2 mm= • 5. 44 x 107 g/8. 1 x 104 mol=
Answers 4 • 4. 99 x 10 kg 5 2 • 3. 71 x 10 mm 2 • 6. 72 x 10 g/mol
Significant Figures
Rules • All non zero digits are significant Ex: 127 • Zeros between significant digits are always significant (sandwich zeros) Ex: 106 • Leading zeros are never significant (placeholder zeros) Ex: 0. 005 • Trailing zeros are significant only if there is a decimal in the number Ex: 25. 30
Copy the examples below and write the number of significant figures 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 7623142516 7084 0. 00761 421. 00 0. 538 5000 5 x 103 5. 0 x 103 5000. 5120
Copy the examples below and write the number of significant figures 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 7623142516 (10) 7084 (4) 0. 00761 (3) 421. 00 (5) 0. 538 (3) 5000 (1) 5 x 103 (1) 5. 0 x 103 (2) 5000. (4) 5120 (3)
Multiplication and Division • The final answer should have the same number of sig figs as the measurement having the smallest number of sig figs Ex: 10. 305 g x 0. 00320 g= Ex: 3. 64928 g/5. 2 m. L=
Addition and Subtraction • Line the numbers up in column form Ex 1: 3. 461728 Ex 2: 467. 384 14. 91 -2. 384 0. 98001 + 5. 2631 Ex 3: 564321 - 264321
Significant Figures Song To the tune of Three Blind Mice
Verse 1 • Addition and Subtraction line numbers up in columns (Repeat) • Make sure the decimals are aligned right, Take off the numbers that are on the right • To get the sig figs (Repeat)
Verse 2 • Multiplication and division count the numbers (Repeat) • Find the one that is the least That’s the number, the rest will cease • To get the sig figs (Repeat)
Complex Conversions
#1 A heater gives off heat at a rate of 330 k. J/min. What is the rate of heat output in kilocalories per hour? (1 cal=4. 184 J)
#1 Answer 3 4. 7 x 10 kcal/h
#2 A water tank leaks water at the rate of 3. 9 m. L/h. If the tank is not repaired, what volume of water in liters will it leak in a year?
#2 Answer 34 L/yr
#3 At the equator, Earth rotates with a velocity of about 465 m/s. What is the velocity in kilometers per hour? What is the velocity in kilometers per day?
#3 Answer 1670 km/hr 4 4. 02 x 10 km/d
Density
Formula • Density=Mass/Volume • D=m/V • If you know the density triangle, you can get the formulas for m and V. • The units of density are always going to have a division sign in them. Ex: g/m. L
Question 1 A block has a volume of 3 25. 3 cm. Its mass is 21. 7 g. Calculate the density of the block.
Answer 0. 858 g/cm 3
Question 2 Isopropyl alcohol has a density of 0. 785 g/m. L. What volume should be measured to obtain 20. 0 g of the liquid?
Answer 25. 5 m. L
Question 3 Ethanol has a density of 0. 785 g/m. L. If you have 105 m. L, how much mass will it have?
Answer 82. 4 g
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