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Chemistry by the numbers

Chemistry by the numbers. Units of Measurement – The Metric System Length: Volume: Mass:. meter. gram. liter. Chemistry by the numbers. What is the mass of an electron? 0.000,000,000,000,000,000,000,000,000,000,911 kg What is the distance between our sun and Pluto?

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Chemistry by the numbers

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  1. Chemistry by the numbers Units of Measurement – The Metric System Length: Volume: Mass: meter gram liter

  2. Chemistry by the numbers What is the mass of an electron? 0.000,000,000,000,000,000,000,000,000,000,911 kg What is the distance between our sun and Pluto? 5,913,520,000,000 m Is there a better way to write these numbers? YES! Scientific Notation

  3. Chemistry by the numbers First, locate the first significant digit Scientific Notation Move this decimal... ...to just after the first significant digit • Then count the places the decimal moved...

  4. Chemistry by the numbers Your new number is then written times 10 to the number of places you moved the decimal Scientific Notation kg • The number is negative because the original number is a decimal So try it with the other number: 5,913,520,000,000 m →

  5. Significant Figures • 2 kinds of numbers: • Exact: The precise amount. • (ie Money in your pocket) • Approximate: Anything MEASURED. • No measurement is perfect

  6. When to use Significant figures • Scientists only use numbers that are reliable. Example: The mass of a coin on a triple-beam balance is 2.7g the mass of the same coin on a digital scale is 2.700g Are they the same number?

  7. When to use Significant figures • To a mathematician, yes. But to a scientist, they are not the same! • 2.700g to a scientist means the measurement is accurate to within one thousandth of a gram. 2.700g • The scale is more accurate and will have more significant figures.

  8. How many sig figs? • Rule: All digits are significant starting with the first non-zero digit on the left. • 1st Exception: In whole numbers that end in zero, the zeros at the end are not significant. Has 4 sig figs Has 3 sig figs Has 1 sig fig ???

  9. How many sig figs? • 7 • 40 • 0.5 • 0.00003 • 7 x 105 • 7,000,000 • 1 • 1 • 1 • 1 • 1 • 1

  10. How do I know how many? • 2nd Exception: Zeroes between two non-zero numbers are significant. • 2002 sec • 3rd Exception: Zeroes to the right of a decimal are significant. • 11.4000kg • 4th Exception: decimal points make all zeroes to the left significant. • 90100. m Has 4 sig figs Has 6 sig figs Has 5 sig figs

  11. How do I know how many? Sig Figs & Scientific Notation Count all the numbers before the x10 9.3x10²cm = 4.1000x10³³kg = 2 5

  12. How many sig figs? • 1.2 • 2100 • 56.76 • 4.00 • 0.0792 • 7,083,000,000 • 2 • 2 • 4 • 3 • 3 • 4

  13. How many sig figs? • 3401 • 2100 • 2100.0 • 5.00 • 0.00412 • 8,000,050,000. • 4 • 2 • 5 • 3 • 3 • 10

  14. Sig Fig Calculations Adding or subtracting measurements • Answer will have no more places after the decimal than the LEAST accurate measurement • but 1.2cm is least accurate with only one place after the decimal. Therefore, round to the one decimal Ex: 2.45 cm + 1.2cm = 3.65cm? 7.432L + 2L 3.7cm = 9.432L round to 9L

  15. Sample Problems • 123.0cm – 99.82cm = • 2100.mL + 101mL = • 88.772g – 17.1g = • 24.00cm – 18cm = • 7234.1m + 1000.0m = • 708g – 8.4g = • 23.2cm • 2201mL • 71.7g • 6cm • 8234.1m • 700g

  16. Sig Fig Calculations • Multiplying or dividing, significant figures Answer will have no more significant figures than the least reliable measurement. 56.780cm x 2.45cm = 139.111 cm2 5 sig figs 3 sig figs Round to 3 sig figs... 139.111 cm2 → 139 cm2 If two numbers have the same reliability, use the least amount of sig figs. 12.12km2 → 12.1km2 12.00km x 1.01km =

  17. Sample Problems • 4cm² • 72cm² • 72.34m/sec • 87.4g/L • 332.12kg • 2600 m • 1.0cm x 4cm = • 4.00cm x 18cm = • 7234.1m ÷ 100.0sec = • 708g ÷ 8.1L = • 298.01kg + 34.112kg = • 84m/s x 31.221s =

  18. Accuracy vs. Precision Accuracy: measurements that are close to the true value. Precision: measurements that are consistent.

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