Measuring

What are Significant Figures Any digit of a number that is known with certainty. They tell you how precise a measurement is. Any digit of a number that is known with certainty. They tell you how precise a measurement is. Recording Sig Figs Recording Sig Figs  Sig figs in a measurement include the known digits plus a final estimated digit cm

Significant Figure Rules  Count all numbers EXCEPT:  Leading zeros *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

, C. Significant Figures Counting Sig Fig Examples , sig figs 3 sig figs 2 sig figs

Applying your rules ? sig figs ? sig figs ? sig figs ? sig figs 60? sig figs 60? sig figs ? sig figs ? sig figs ? sig figs ? sig figs ? sig figs ? sig figs

Applying your rules sig figs sig figs sig figs sig figs 601 sig figs 601 sig figs sig figs sig figs sig figs sig figs sig figs sig figs

Significant Figure Rules cont. Calculating with Sig Figs Calculating with Sig Figs  Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm 3 ) * (23.3cm 3 ) = g 324 g 4 SF3 SF

Significant Figure Rules cont. Calculating with Sig Figs (con’t) 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 mL mL 7.85 mL  7.9 mL 3.75 mL mL 7.85 mL

Significant Figure Rules cont.  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

1. (15.30 g) ÷ (6.4 mL) = g/mL  18.1 g g g g 4 SF2 SF  2.4 g/mL 2 SF Practice Problems

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.

Examples Make the following into a 3 Sig Fig number ,  ,  10 6 Your Final number must be of the same value as the number you started with, 129,000 and not 129

Examples of Rounding For example you want a 4 Sig Fig number , 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 ,

Scientific Notation Converting into Sci. Notation: Converting into Sci. Notation:  Move decimal until there’s 1 digit to its left. (1-9) Places moved = exponent. 65,000 kg  6.5 × 10 4 kg Only include sig figs.

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

Scientific Notation 1. 2,400,000  g kg 3.7  km  10 4 mm Practice Problems 2.4  10 6  g 2.56  kg km 62,000 mm

Scientific Notation Calculating with Sci. Notation Calculating with Sci. Notation (5.44 × 10 7 g) ÷ (8.1 × 10 4 mol) = 5.44 EXP EE ÷ ÷ EXP EE ENTER EXE = = 670 g/mol= 6.7 × 10 2 g/mol Type on your calculator:

SI Prefix Conversions 1.Find the difference between the exponents of the two prefixes. 2.Move the decimal that many places. 3.Be sure to maintain sig figs! To the left or right?

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King - Kilometer1000m10 3 King - Kilometer1000m10 3 Henry- Hectometer100m10 2 Henry- Hectometer100m10 2 Died - Decameter10m10 1 Died - Decameter10m10 1 By - Base Unit1m10 0 By - Base Unit1m10 0 Drinking - Decimeter.1m Drinking - Decimeter.1m Chocolate - Centimeter.01m10 -2 Chocolate - Centimeter.01m10 -2 Milk - Millimeter.001m10 -3 Milk - Millimeter.001m10 -3 Copyright © 2010 Ryan P. Murphy

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

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

Dimensional Analysis Steps: 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.

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