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Aim: How can we convert numbers into scientific notation and help with significant figures?

Aim: How can we convert numbers into scientific notation and help with significant figures?. Do Now The speed of light is 300,000,000 m/s How would this look in scientific notation?. The answer will be known shortly. SCIENTIFIC NOTATION

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Aim: How can we convert numbers into scientific notation and help with significant figures?

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  1. Aim: How can we convert numbers into scientific notation and help with significant figures? Do Now The speed of light is 300,000,000 m/s How would this look in scientific notation? The answer will be known shortly

  2. SCIENTIFIC NOTATION Illustrates numbers by orders of magnitude (Powers of 10) 100 = 101 = 102 = 1 10 100 10-1 = 10-2 = 10-3 = 0.1 or 1/10 0.01 or 1/100 0.001 or 1/1,000

  3. Scientific Notation Form: • M x 10n • Rules: • M must only have 1 non-zero digit to the left of the decimal. • Example: 3.24 x 102 is correct • 32.4 x 101 is incorrect • 0.324 x 103 is incorrect

  4. Add a power of 10 every time you move the decimal point one place to the left • Example: 45,625 (this is really 45,625 x 100) 4 3 2 1 4.5625 x 104 3. Subtract a power of 10 every time you move the decimal point one place to the right Example: 0.00538 (this is really 0.00538 x 100) 1 2 3 5.38 x 10-3 Do Now: 300,000,000 x 100 = 3.0 x 108 Who was right?

  5. Convert the following to standard notation: • 5.5 x 104 • 8.321 x 10-3 • 2.1 x 109 • 3.8 x 10-5 55,000 0.008321 2,100,000,000 0.000038 • Convert the following to scientific notation: • 9,508 • 0.000607 • 10,501 • 0.025 9.508 x 103 6.07 x 10-4 1.0501 x 104 2.5 x 10-2

  6. Only reliable accurate digits can be in scientific notation. These are known as significant digits (significant figures)

  7. Rules: • All non-zero digits are significant • Ex: 112.832 • 6 sig. figs. • All zeros between non-zeros are significant • Ex: 1003.01 • 6 sig. figs. • 3. All final zeros before a decimal and beginning zeros are not significant • Ex: 300,000,000 • 1 sig. fig. • 0.000098 • 2 sig. figs.

  8. 4. All final zeros after a decimal are significant • Ex: 25.00 • 4 sig. figs. • How many sig. figs. are in each of the following: • 9,500 • 0.0090080 • 10,201.06 • 6.2 x 106 2 5 7 2

  9. Take out your calculators Do you know how to use your calculator correctly? Your calculator has a button that either says EE or EXP This button means times ten to the Ex: 3.97 x 1014 x 2.86 x 10-17 = This is how you type it: 3.97 EE 14 x 2.86 EE ± 17 = or 3.97 EXP 14 x 2.86 EXP (-) 17 =

  10. Pages for Additional Reading • Pages 28, 31

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