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Writing Numbers in Scientific Notation and Using Significant Figures

Bell Ringer: Oct. 4, 2010: Complete the table below. Place X in the appropriate box to indicate the type of each measurement unit. Reference: Physical Science, page 16. Writing Numbers in Scientific Notation and Using Significant Figures. Glenn C. Soltes Integrated Science Biology 2010-2011.

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Writing Numbers in Scientific Notation and Using Significant Figures

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  1. Bell Ringer: Oct. 4, 2010: Complete the table below. Place X in the appropriate box to indicate the type of each measurement unit. Reference: Physical Science, page 16

  2. Writing Numbers in Scientific Notation and Using Significant Figures Glenn C. Soltes Integrated Science Biology 2010-2011

  3. Objectives: • Define Scientific Notation and Significant Figures. • Identify the rules in writing scientific notation and significant figures. • Use scientific notation and significant figures in problem solving. • Identify the significant figures in calculations.

  4. Scientific Notation A short-hand way of writing large numbers without writing all of the zeros.

  5. A number is expressed in scientific notation when it is in the form a x 10n where a is between 1 and 10 and n is an integer

  6. The Distance From the Sun to the Earth 93,000,000 miles

  7. How to write scientific Notation

  8. Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1

  9. 2.10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 1023

  10. Write 28750.9 in scientific notation. • 2.87509 x 10-5 • 2.87509 x 10-4 • 2.87509 x 104 • 2.87509 x 105

  11. 2) Express 1.8 x 10-4 in decimal notation. 0.00018 3) Express 4.58 x 106 in decimal notation. 4,580,000 On the graphing calculator, scientific notation is done with the button. 4.58 x 106 is typed 4.58 6

  12. Practice Problem Write in scientific notation. Decide the power of ten. • 98,500,000 = • 64,100,000,000 = • 279,000,000 = • 4,200,000 = • .000567 =

  13. Significant Figures A prescribed decimal place that determines the amount of rounding off to be done based on the precision of the measurement.

  14. There are 2 kinds of numbers: • Exact: the amount of money in your account. Known with certainty.

  15. Approximate: weight, height—anything MEASURED. • No measurement is perfect.

  16. When a measurement is recorded only those digits that are dependable are written down.

  17. If you measured the width of a paper with your ruler you might record 21.7cm. To a mathematician 21.70, or 21.700 is the same.

  18. But, to a scientist 21.7cm and 21.70cm is NOT the same • 21.700cm to a scientist means the measurement is accurate to within one thousandth of a cm.

  19. If you used an ordinary ruler, the smallest marking is the mm, so your measurement has to be recorded as 21.7cm.

  20. How do I know how many Significant Figures?

  21. RULES:

  22. Rule: All digits are significant starting with the first non-zero digit on the left.

  23. Exception to rule: In whole numbers that end in zero, the zeros at the end are not significant.

  24. 7 40 0.5 0.00003 7 x 105 7,000,000 1 1 1 1 1 1 How many significant figures?

  25. 2nd Exception to rule: If zeros are sandwiched between non-zero digits, the zeros become significant.

  26. 1.2 2100 56.76 4.00 0.0792 7,083,000,000 2 2 4 3 3 4 How many significant figures here?

  27. 3401 2100 2100.0 5.00 0.00412 8,000,050,000 4 2 5 3 3 6 How many sig figs here?

  28. Practice: Count the number of significant figures. 1. 80000 2. 0.0015 3. 8 002 000 4. 1.12 5. 1.oo5

  29. What about calculations with significant figures?

  30. Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.

  31. Add/Subtract examples • 2.45cm + 1.2cm = 3.65cm, • Round off to = 3.7cm • 7.432cm + 2cm = 9.432 round to  9cm

  32. Multiplication and Division • Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

  33. A couple of examples • 56.78 cm x 2.45cm = 139.111 cm2 • Round to  139cm2 • 75.8cm x 9.6cm = ?

  34. Perform the following calculations, and write the answer with the correct number of significant figures. • a. 12.65 cm x 42.1 cm • b. 3.02 cm x 6.3 cm x 8.225 cm • c. 3.7 g ÷ 1.o83 cm3

  35. End Credit: Holt, Physical Science 2006

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