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Scientific Organization of Measurements

Scientific Organization of Measurements. Significant Digits and Scientific Notation. Significant Digits. consist of all of the digits known with certainty plus one final digit that is estimated. Many experiments in science involve measuring different quantities. No

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Scientific Organization of Measurements

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  1. Scientific Organization of Measurements Significant Digits and Scientific Notation

  2. Significant Digits consist of all of the digits known with certainty plus one final digit that is estimated Many experiments in science involve measuring different quantities. No matter how carefully scientists measure something, there is always a limit to how exact, or precise, a measurement is. This limits how precise the results of the experiment are. For this reason, scientists use significant figures to keep track of the precision of their calculations.

  3. Significant Digits

  4. Find the number of significant digits: • a. 0.003 26 • b. 39 010 • c. 77 900.1 • d. 1.5300 • a. 3 • b. 4 • c. 6 • d. 5

  5. Calculations with Sig Figs • Adding and Subtracting with Significant Figures The answer must have the same number of digits to the right of the decimal as there are in the measurement having the fewest digits to the right of the decimal point. • Multiplication and Division with Significant Figures The answer can have no more sig figs than are in the measurement with the fewest total sig figs

  6. 1. 3.45 cm3 + 8.0654 cm3 2. 8.9 kg/L x 0.9753 L 3. 46.98 m – 18.114 m 4. 28 m x 16.45 m 5. 418.20 g /63.9 cm3 1. 11.52 cm3 2. 8.7 kg 3. 28.87 m 4. 460 m2 5. 6.54 g/cm3 Express each answer to the correct number of significant figures

  7. Scientific Notation • A method of representing very large or very small numbers M x 10n • M is a number between 1 and 10 • n is an integer • all digits in M are significant Science often deals with large numbers. The number of hydrogen atoms in a liter of water, for example, is almost 70 000 000 000 000 000 000 000 000. On the other hand, the width of our galaxy is 9 315 000 000 000 000 km. To write out such huge numbers every time you used them would be a lot of trouble. If you were performing a series of calculations, working with long numbers could be time-consuming and confusing.

  8. a. 325 kg b. 0.000 46 m c. 7104 km d. 0.0028 L 3.25 x 10 2 4.6 x 10 -4 7.104 x 10 3 2.8 x 10 -3 Convert the following measurements to scientific notation:

  9. Scientific Notation • Reducing to Scientific Notation 1. Move decimal so that M is between 1 and 10 2. Determine n by counting the number of places the decimal point was moved a. Moved to the left, n is positive b. Moved to the right, n is negative

  10. Mathematical Operations Using Scientific Notation • 1. Addition and subtraction • Operations can only be performed if the exponent on each number is the same • 2. Multiplication • M factors are multiplied • Exponents are added • 3. Division • M factors are divided • Exponents are subtracted (numerator - denominator)

  11. Solve the following 1. (2.8 x 10 5)(7.53 x 10 -6) ________________________ 2. (3.1 x 10 -2) (4.380 x 10 3) ________________________ 3. (4.20 x 10 2) (0.040 x 10 -1) ________________________ 4. 3.0 x 10 3 ÷ 1.2 x 10 4 ________________________ 5. 4.95 x 10 6 ÷ 2.33 x 10 -2 ________________________

  12. 1. (2.8 x 10 5)(7.53 x 10 -6) 2. (3.1 x 10 -2) (4.380 x 10 3) 3. (4.20 x 10 2) (0.040 x 10 -1) 4. 3.0 x 10 3 ÷ 1.2 x 10 4 5. 4.95 x 10 6 ÷ 2.33 x 10 -2 2.1 x 10 0 1.4 x 10 2 1.7 x 10 0 2.5 x 10 -1 2.12 x 10 8

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