1 / 30

Scientific Notation & Dimensional Analysis

Scientific Notation & Dimensional Analysis. Chapter 2.2. Objectives. I can recognize numbers in scientific notation . I can convert between numbers in standard form and scientific notation . I can perform mathematical manipulations on numbers in scientific notation.

todd-boone
Download Presentation

Scientific Notation & Dimensional Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Scientific Notation &Dimensional Analysis Chapter 2.2

  2. Objectives • I can recognize numbers in scientific notation. • I can convert between numbers in standard form and scientific notation. • I can perform mathematical manipulations on numbers in scientific notation. • I can use dimensional analysis to convert between units.

  3. What is scientific notation? • A short-hand way to write a very small or large number without all the zeros. • 0.00000000000000678 = 6.78x10-15 • 7958900000000 = 7.9589x1012 • Numbers expressed as a multiple of two factors. • A number between 1 to 10 and ten raised to a power. • The exponent or power tells you how many times the first factor must be multiplied by 10. • For numbers > 1→ positive (+) exponent • For numbers < 1 → negative (-) exponent

  4. Converting data into scientific notation • STEP 1→ Move the decimal place so the number is between 1 and 9. • STEP 2→ Remove any extra zeros at the end or beginning or the number. • STEP 3→ Multiply the result by 10n where n is the number of decimal places moved. • If the number was less than 1, then n will be negative. • (The decimal place moved to the right). • If the number was greater than 1, then n will be positive. • (The decimal place moved to the left).

  5. EXAMPLE:The Distance From the Sun to the Earth 93,000,000 miles

  6. Step 1 • Move decimal • Leave only one number in front of decimal 93,000,000 = 9.3000000

  7. Step 2 • Write number without zeros 93,000,000 = 9.3

  8. 7 93,000,000 = 9.3 x 10 Step 3 • Count how many places you moved decimal • Make that your power of ten

  9. The power of ten is 7 because the decimal moved 7 places to left. 93,000,000 = 9.3 x 107 • 93,000,000 miles → Standard Form • 9.3 x 107 miles → Scientific Notation

  10. Practice Problems Write the number in scientific notation. • 734,000,000 • 870,000,000,000 • 90,000,000,000 • 0.00000765 • 0.00000000034 = 7.34 x 108 = 8.7 x 1011 = 9.0 x 1010 = 7.65 x 10-6 = 3.4 x 10-10

  11. Converting data out of scientific notation • Move the decimal place the number of places indicated by the exponent. • If exponent is negative, the decimal place will move to the left and the result will be less than 1. • If exponent is positive, the decimal place will move to the right and the result will be greater than 1.

  12. Practice Problems Write the number in standard form. • 9.5 x 106 • 5.47 x 10-4 • 6.775 x 1010 = 9,500,000 = 0.000547 = 67,750,000,000

  13. Using a calculator for scientific notation • The EE button on your calculator will allow you to enter a number in scientific notation. EXAMPLE → 3.95 X 10-7 • Enter 3.95 • Press EE • Enter (-) • Enter 7 • Proceed with manipulation as usual.

  14. Adding and Subtracting • The exponents MUST be the same. If they are not, convert the numbers by moving the decimal point and adjusting the exponent. • Then, add or subtract the quantities. • Remember to readjust the answer back to scientific notation at the end of the problem if the factor is no longer between 1 and 9. • Also remember sig figs rules of adding and subtracting apply from the original numbers. The answer should have the number of decimal places as the least of the original numbers.

  15. Adding and Subtracting Add 2.7 x 107, 5.35 x 106 , & 7.49 x 108 2.700 x 107 0.535 x 107 74.900 x 107 78.135 x 107 Final answer must have same number decimal places as least original number and factor must be between 1 and 9 + FINAL ANSWER: 7.8 x 108

  16. Multiplying and Dividing • Multiplication: Multiply the factors first, than add the exponents. • Division: Divide the factors first, then subtract the exponents. • Remember to readjust the answer back to scientific notation at the end of the problem if the factor is no longer between 1 and 9. • Also remember sig figs rules of multiplication and division apply from the original numbers. The answer should have the same number of sig figs as the least of the original numbers.

  17. Multiplying and Dividing Divide 5.65 x 107 by 3.9 x 10-3 Final answer must have same number sig figs as least original number and factor must be between 1 and 9

  18. Dimensional Analysis How to convert from one set of units to another AKA Factor Label Method

  19. What is a conversion factor? • Two numbers that are equivalent but written in different units. • Written as a fraction and the same no matter which number is written on top. Example: 365 days = 1 year

  20. Steps of Dimensional Analysis • Read the problem. • Determine the given. • Determine the unknown. • Think about the conversions factors that you know to get from the given to the unknown.

  21. Example: How many yards are in 56 inches? 56 inches Write the given with it’s unit in the first numerator of your “railroad” track.

  22. What conversion factors do you know that will get you closer to the unit you want in the final answer? • I have 56 inches • I want yards Have Want I Know (conversion factors) I know12 in = 1 foot and 3 feet = 1 yard

  23. 56 inches inches • Pick a conversion factor that will get you closer to the unit you want in the final answer. This becomes the unit at the top of the new fraction. • I know 12 inches = 1 foot 1 foot 12

  24. Is the unit on TOP the one you WANT to end up with? YES • then do the math find another conversion factor that gets you closer NO

  25. 1 foot 12 56 inches inches • My “given” unit cancelled and I’m left with feet. • I WANT yards • I HAVE feet 1 yard 3 feet I KNOW 3 feet = 1 yard so . . .

  26. 1 foot 12 56 inches 1 yard inches 3 feet • The last step is to check your cancelled units and do the math! • 56 x 1 x 1 ÷ 12 ÷ 3 = 1.6 yards • Congratulations! Now you can solve word problems by dimensional analysis!

  27. Rules of Dimensional Analysis • Write ALL numbers as fractions. • Include units with all numbers (No Naked Numbers!). • Figure out what conversion factors are needed to get to the wanted units. • Arrange conversion factors so the units cancel. • Set up the entire problem first, then do the math. • Multiply the numbers on top (avoid calculation error-don’t stop in middle of calculation). • Divide result of top by result of bottom. Show WORK and DON’T skip steps.

  28. If you are 16 years old, what is your age in seconds? • Given: 16 years • Wanted: Age in seconds • Conversion factors: days/yr, hours/day, minutes/hour, & seconds/minutes = 504576000 seconds What is that in scientific notation and sig figs? = 5.0 x 108 seconds

  29. You want download your music collection to iTunes. You have 225 CDs. If each CD has 12 songs and it takes 85 seconds to download 1 song, how many hours will it take to download your entire collection? • Given: 225 CDs • Wanted: Hours to Download • Conversion factors: songs/CD, sec/song, sec/min, min/hour =63.75 hours

  30. The density of copper is 8.96 g/mL. What is its density in kg/m3? =8960 kg/m3 or 8.96 x 103 kg/m3

More Related