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C. What are Significant Figures

Learn how to count, calculate, and round with significant figures in this comprehensive guide. Understand the rules, practice problems, and conversions with SI prefixes and scientific notation.

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C. What are Significant Figures

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  1. C. What are Significant Figures • The places in the numbers that are important. They tell you how precise a measurement is. • Recording Sig Figs • Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm

  2. C. Significant Figures • Count all numbers EXCEPT: • Leading zeros -- 0.0025 *Decimal present start from left until you get your first non zero number • Trailing zeros without a decimal point -- 2,500 *Decimal absent start from right until you get your first non zero number

  3. C. Significant Figures Counting Sig Fig Examples 1. 23.50 1. 23.50 4 sig figs 3 sig figs 2. 402 2. 402 3. 5,280 3. 5,280 3 sig figs 2 sig figs 4. 0.080 4. 0.080

  4. Applying your rules • 520.36 ? sig figs • 1.00250 ? sig figs • 60 ? sig figs • 458200000 ? sig figs • 0.250000 ? sig figs • 0.0063000 ? sig figs

  5. Applying your rules • 520.36 5 sig figs • 1.00250 6 sig figs • 60 1 sig figs • 458200000 4 sig figs • 0.250000 6 sig figs • 0.0063000 5 sig figs

  6. 3 SF C. Significant Figures • Calculating with Sig Figs • Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm3) * (23.3cm3) = 324.103g 4 SF 3 SF 324g

  7. C. Significant Figures • Calculating with Sig Figs (con’t) • Add/Subtract – same # of digits to the rights of the decimal as the measurement with the smallest # of digits to the right of the decimal. 224 g + 130 g 354 g 224 g + 130 g 354 g 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL  350 g  7.9 mL

  8. C. Significant Figures • Exact Numbers do not limit the # of sig figs in the answer. • Counting numbers: 12 students • Exact conversions: 1 m = 100 cm • “1” in any conversion: 1 in = 2.54 cm

  9. 5. (15.30 g) ÷ (6.4 mL)  2.4 g/mL 2 SF C. Significant Figures Practice Problems 4 SF 2 SF = 2.390625 g/mL 6. 18.9 g - 0.84 g  18.1 g 18.06 g

  10. Rounding! RULE 1. If the first digit you remove is 4 or less, drop it and all following digits. RULE 2. If the first digit removed is 5 or greater, round up by adding 1 to the last digit kept. If a calculation has several steps, it is best to round off at the end. Chapter Two

  11. Practice Rule #2 Rounding Your Final number must be of the same value as the number you started with, 129,000 and not 129 1.5587 .0037421 1367 128,522 1.6683 106 1.56 .00374 1370 129,000 1.67 106 Make the following into a 3 Sig Fig number

  12. Examples of Rounding 0 is dropped, it is <5 8 is dropped, it is >5; Note you must include the 0’s 5 is dropped it is = 5; note you need a 4 Sig Fig 4965.03 780,582 1999.5 4965 780,600 2000. For example you want a 4 Sig Fig number

  13. Scientific Notation 65,000 kg  6.5 × 104 kg • Converting into Sci. Notation: • Move decimal until there’s 1 digit to its left. (1-9) Places moved = exponent. • Only include sig figs.

  14. Large # (>1)  positive exponent • (move to the left) • Small # (<1)  negative exponent • (move to the right) • To work backwards from scientific notation to decimal notation just do the opposite.

  15. 7. 2,400,000 g 8. 0.00256 kg 9. 7  10-5 km 10. 6.2  104 mm Scientific Notation Practice Problems 2.4  106 g 2.56  10-3 kg 0.00007 km 62,000 mm

  16. EXE EXP EXP ENTER EE EE Scientific Notation • Calculating with Sci. Notation (5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your calculator: 5.44 7 8.1 4 ÷ = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

  17. To the left or right? A. SI Prefix Conversions 1. Find the difference between the exponents of the two prefixes. 2. Move the decimal that many places.

  18. NUMBER = UNIT A. SI Prefix Conversions 0.532 532 m = _______ km NUMBER UNIT

  19. kilo- mega- M k 106 103 deci- BASE UNIT d --- 100 10-1 centi- c 10-2 milli- m 10-3 micro-  10-6 nano- n 10-9 pico- p 10-12 A. SI Prefix Conversions Prefix Symbol Factor move left move right

  20. 1) 20 cm = ______________ m 2) 0.032 L = ______________ mL 3) 45 m = ______________ nm 4) 805 dm = ______________ km A. SI Prefix Conversions 0.2 32 45,000 0.0805

  21. Dimensional Analysis • The “Factor-Label” Method • Units, or “labels” are canceled, or “factored” out

  22. Dimensional Analysis • Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

  23. cm yd Dimensional Analysis 1 in = 2.54 cm 1 ft = 12 in 1 yd = 3 ft 1. Taft football needs 550 cm for a 1st down. How many yards is this? 1 ft 12 in 1 yd 3 ft 1 in 2.54 cm 550 cm = 6.0 yd

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