Significant Figures and Scientific Notation Significant Figures All

Significant Figures and Scientific Notation

Significant Figures § All measurements are inaccurate § Precision of measuring device § Human error § Faulty technique

Significant Figures § Measurements need to convey precision § Must include degree of uncertainty § Sig Figs tell us

Significant Figures

Significant Figures 1. Significant figures in a measurement include § § all of the digits that are known precisely plus one last digit that is estimated.

Significant Figures 2. Non-zero digits are always significant. 103. 230002

Significant Figures 3. All final zeros after the decimal point are significant. 12. 740 0. 0420

Significant Figures 4. Zeros between two other significant digits are always significant. 10. 0 2004 6. 000

Significant Figures 5. Zeros used only for spacing the decimal point are not significant. 100 0. 00000233

§ Always put a 0 in front of a decimal point § 0. 0042 §. 873 § 0. 247

Scientific notation § Some numbers are VERY big or VERY small. We use Sci. Note. To make them shorter. §

§ To put a number in Scientific notation, drag the decimal until there is only ONE non-zero number in front of it. § Add x 10 y to the end § The exponent y is determined by the number of times you moved the decimal and which direction.

§ If the decimal moves left, the exponent is positive. § If it moves right, it is negative. § Sci. Note. ONLY keeps the sig. fig. amount.

§ Examples: § 4000 will become 4 x 103 § 567. 3 will become 5. 673 x 102 § 0. 0000035 will become 3. 5 x 10 -6 § 0. 000780 will become 7. 80 x 10 -4

Significant Figures 6. If you add or subtract, the answer is rounded to the same number of decimal places as the measurement with the least number of decimal places.

Significant Figures 7. If you multiply or divide two numbers, the answer is rounded off to the number of significant figures in the least precise term used in the calculation (i. e. the number with the fewest sig figs).

Calculations

Calculations