1.3 NOTES Scientific Measurement

Why is it important to standardized measurment?

What’s the problem? Really? What?

The Metric System SI Units- International system, used for continuity   Base units 7 base units

Derived units Units made up of two or more base units Examples: volume (L x W x H, m3), area (L x W, m2), velocity (m/s), density (g/mL)

The formula can be rearranged to solve for any of the variables Density Relates mass and volume Density = Mass D = M Volume V The formula can be rearranged to solve for any of the variables Example 1: What is the volume of a sample that has a mass of 20 grams and a density of 4 g/mL? Example 2: A piece of metal with a mass of 147 g is placed in a 50 mL graduated cylinder. The water level rises from 20 mL to 41 mL. What is the density of the metal

Significant Figures Measurements are only as accurate and precise as the instrument that produced it The number of significant figures in a measurement is an indication of accuracy. For example, if you measure the length of a room by pacing it, your measurement will have less accuracy than if you measure it with a steel measuring tape, and the measurements recorded will have different numbers of significant figures. When pacing, you might record the length as 7 meters, a measurement with one significant figure. Using the tape, you might record the measurement as 7.27 meters, accurate to 3 significant figures.

Rules of significant figures (sig figs): All nonzero digits are significant. 16.2 g has 3 significant figures Zeros: Zeros between 2 nonzero digits are always significant. Zeros between 2 significant digits are significant. e.g. 505mm has 3 sig figs Trailing zeros (those at the right end of a whole number) are significant only if there is a decimal after the zero or if there is a bar over the zero. E.g. 20. L, or 2000 kg All zeros after a decimal are significant only if there is a nonzero digit somewhere to the left of the zero. e.g. 1.0 has 2 sig figs; .005 has only 1 sig fig Leading zeros (those that precede nonzero digits) are placeholders and are never significant. e.g. 0.004 has 1 sig fig   Exact numbers, such as the 60 and the 1 in the sentence “60 min = 1 hour” have an infinite number of significant digits. Counting numbers such as “1 atom” have infinite significance. When numbers are in scientific notation, the only significant part is what comes before the x10. For example, 2.3 x 103 has 2 sig figs, and 2.0000 x 1010 has 5.

How many significant figures are present in the following numbers? 345 400 2.00 x 105 Method #2 - .L ----------------------R   2.001 0.001 1000.

Rules of significant figures (sig figs): Rounding Always look to the number to the right of the last number you are keeping. If the number to the right is from 0-4, the last number stays the same. If the number to the right is from 5-9, the last number rounds up. Examples:   Round the following to 3 significant figures: 43201  Round the following to 3 significant figures: 43.259  Round the following to 4 significant figures: 43.259 

Rules of significant figures (sig figs): Adding and subtracting Round your final answer to the least number of decimal places present in the factors Examples: 1.2 1.0001 + 3.45 + 3.297

Rules of significant figures (sig figs): Round your final answer to the least number of significant figures present in the factors Examples: 49 / 7 = 5 X 5 = 147 / 7.0 =

Scientific Notation 1524  .00043  A method of taking very large numbers or very small numbers and making them manageable To put numbers in scientific notation, move the decimal so that only one number is in front of the decimal, with all other numbers behind the number Examples 1524    .00043 

Scientific Notation Adding and subtracting The exponent must be the same for all numbers you are adding and subtracting Add the decimal portion together and keep the exponent the same Examples: 5.2 X 106 8.14 X 109 1.2 X 103 + 1.3 X 106 - 6.01 X 109 + 1.2 X 104  

Scientific Notation Multiplication Multiply the decimal portion together Add the exponents Examples: (6 X 103) X (1 X 106) = (1.2 X 103) X (4.1 X 102) =   (1.2 X 10-2) X (4.1 X 10-4) =

Scientific Notation Division 8 X 106 9 X 103 4 X 104 3 X 10-3 Divide the decimal portion Subtract the exponents Examples: 8 X 106 9 X 103 4 X 104 3 X 10-3

Metric Prefixes Prefix Exponential Factor Meaning - Example Kilo 103 1 000m = 1 kilometer Hecta 102 100m = 1 hectometer Deka 101 10m = 1 decameter Base Unit 100 1 meter = 1 meter Deci 10-1 .1 meter = 1 decimeter Centi 10-2 .01 meter = 1 centimeter Milli 10-3 .001 meter = 1 millimeter

Prefixes are used to represent quantities that are larger or smaller than the base units

Metric Prefixes When you convert between two units, move the decimal. When going from a small unit to a larger unit, your number should get smaller. When going from a large unit to a smaller unit, the number should get smaller. King Henry Died By Drinking Chocolate Milk   Kilo Hecta Deka Base Deci Centi Milli

Metric Prefixes Examples: 2.44 cm  km 3.57 g  mg   14 dam  hm 5.46 dL  kL