Metric Systems and Significant Figures Mrs. Charniauskaya

Metric System Scientists all over the world use the same system of units so they can communicate information clearly This system is called Système Internationale d’Unités (SI) Metric measurement is based on the number of 10 and makes calculations easier.

Base Metric Units Measurement Unit of Measurement Length Meter (m) Mass Gram (g) Time Second (s) Volume Liter (L or l)

  What unit (millimeter, centimeter, meter, or kilometer) would be most appropriate for describing the following:       a.  The thickness of a piece of paper   ________________       b.  The length of your pencil     _______________________       c.  The distance from Chicago to L.A.   ________________       d.  The height of the classroom door  ___________________       e.  The width of a textbook   ___________________       f.  The height of the flagpole    ____________________       g.  The thickness of a penny   ____________________      

Units According to Système Internationale d’Unités (SI) 1960 there are base and derived units. Base unit is based on a object or event in a physical world and is independent of other units. Examples: meter (length of an object); kilogram (mass of an object); second (time and event takes). Derived unit is developed from base units (made of two or more base units). Examples: 𝒎 𝒔 , 𝒎𝒆𝒕𝒆𝒓 𝒔𝒆𝒄𝒐𝒏𝒅 (speed); 𝒈 𝒄𝒎 𝟑 , 𝒈𝒓𝒂𝒎 𝒄𝒖𝒃𝒊𝒄 𝒄𝒆𝒏𝒕𝒊𝒎𝒆𝒕𝒆𝒓 (density); 𝒄𝒎 𝟑 (volume)

Units SI Base Units Quantity Base Unit Time Second (s) Length Meter (m) Mass Kilogram (kg) Temperature Kelvin (K) Amount of substance Mole (mol) Electric Current Ampere (A) Luminous Intensity Candela (cd)

Units Derived Units A unit that is defined by a combination of base unit is called derived unit, Volume is the space occupied by an object. Cubic centimeter (cm3) Milliliter (mL or ml) Liter (L or l) 1 cm3 = 1 ml Si Unit Other Unit Used Volume m3 cm3, mL, L

Units of density are derived from base units of mass and length. Units: Derived Units Density is how much mass an object has per unit of volume, the degree of compactness of a substance. https://phet.colorado.edu/en/simulation/legacy/density Density of an object is equal to its mass divided by its volume. 𝑫= 𝒎 𝑽 𝑫= 𝒈 𝒎𝒍 = 𝒈 𝒄𝒎 𝟑 Units of density are derived from base units of mass and length.

Metric Prefix Metric Prefixes make base unit smaller or larger. Kilo Hecto Deka Base Unit Deci Centi Milli k H Da d c m 1000 100 10 1 0.1 0.01 0.001 103 102 101 10-1 10-2 10-3 𝟏𝟎𝟎𝟎 𝟏 𝟏𝟎𝟎 𝟏 𝟏 𝟏 𝟏 𝟏𝟎 𝟏 𝟏𝟎𝟎 𝟏 𝟏𝟎𝟎𝟎

Metric Prefixes Prefix Symbol Numerical Value Power of 10 equivalent To explain the range of a measurement, scientists add prefixes to the base units. Prefix Symbol Numerical Value Power of 10 equivalent Kilo k 1000 103 1 100 Deci d 0.1 10-1 Centi c 0.01 10-2 Milli m 0.001 10-3 Micro μ 0.000001 10-6 Nano n 0.000000001 10-9

Metric Prefixes Kilo- Hecto- Deka- Base Deci- Centi- Milli- 1 cm = 10 mm 1 mm = 0.1 cm Each unit is 10 times larger than the previous one. Each unit is 10 times smaller than the previous one.

Relationship between metric units 1 kg = 1000 g 1g = 10 dg 1g = 100 cg 1 g = 1000 mg 1 km = 1000 m 1 m = 10 dm 1 m = 100 cm 1 m = 1000 mm 1 kL = 1000 L 1 L = 10 dL 1 L = 100 cL 1 L = 1000 mL

Uncertainty in measurements What is the length of the blue object? 1.24 cm? 1.245 cm? 1.25 cm? Which digits are we certain about? Which digit we are uncertain about? A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty. Uncertainty in measurements

Uncertainty in measurements Measurements are performed with instruments. No instrument can read to an infinite number of decimal places.

Significant figures Scientists use significant figures to take into account uncertainty of measurement. In measurements, the significant figures are all the digits that are known, plus a digit that is estimated. 2 sig fig. 3 sig fig.

Rules for Counting Significant Figures Nonzero integers always count as significant figures. 3456 has 4 sig figs.

significant figures. 0.0486 has 3 sig figs. Zeros Leading zeros do not count as significant figures. 0.0486 has 3 sig figs. Leading zeros

16.07 has 4 sig figs. significant figures. Zeros Captive zero Captive zeros always count as significant figures. 16.07 has 4 sig figs. Captive zero

Zeros Trailing zeros are significant only if the number contains a decimal point. 9.300 has 4 sig figs. Trailing zeros

Zeros Trailing zeros are not significant if the number does not contain a decimal point. 9300 has 2 sig figs. Trailing zeros

There are two situations in which a number has a unlimited number of significant figures: Counted numbers are exact. 27 people in your classroom. 275000 people in a city (all figures are significant) Exactly defined quantities. 1 inch = 2.54 cm 1 h = 60 min

When scientist report measurements values they must report correct number significant figures. The correct volume is 56.0 ml, or 55.9 ml, or 56.1 ml The values of 56 ml or 55.95 ml are incorrect, because of incorrect number of sig. figs.

Honors Chemistry, September 9, 2016 Bell Work: Present as a scientific notation 0.00003506 Present as a standard (expanded) notation 7.59 × 𝟏𝟎 −𝟑 58674 mL into L How many sig. figs.: 0.000609 689000 Learning Objective; Be able to perform calculations with the sig. figs. Agenda: Bell Work HW check and review Quiz Calculations with sig. figs. Practice

When scientists do the calculations with the measured values they are coming up with the unreasonable number of significant figures. Mass of an object 6.52 g Object’s volume is 1.3 cm3 𝑫= 𝒎 𝑽 = 6.52 g 1.3 cm3 =𝟓.𝟎𝟏𝟓𝟑𝟖𝟒𝟔𝟏𝟓𝟑𝟖𝟒𝟔𝟏𝟓 𝒈 𝒄𝒎 𝟑 Does the value for density look reasonable? What do we need to do?

Rounding To round a number, decide how many significant figures the answer should have. It depends On given measurement On type of calculation

Multiplication and Division: # sig figs in the result equals the lowest number of sig figs in the calculation. Mass of an object 6.52 g (3 sig. fig.) Object’s volume is 1.3 cm3 (2 sig. fig.) The answer should have 2 sig. figs. 𝑫= 𝒎 𝑽 = 6.52 g 1.3 cm3 =𝟓.𝟎𝟏𝟓𝟑𝟖𝟒𝟔𝟏𝟓𝟑𝟖𝟒𝟔𝟏𝟓 𝒈 𝒄𝒎 𝟑 = 5.0 𝒈 𝒄𝒎 𝟑

Lowest number of decimal places Rounding Addition and Subtraction: The number of decimal places in the result equals the lowest number of decimal places in the calculation. 6.8 + 11.934 = 18.734 = 18.7 Lowest number of decimal places One decimal place One decimal place

Accuracy and Precision

Accuracy and Precision Accuracy refers to how close a measured value is to an accepted value. Precision refers to how close a series of measurements are to one another.

Percent Error Percent error is calculated to know how measured or calculated value is close to accepted (true) value. %𝒆𝒓𝒓𝒐𝒓= 𝒆𝒓𝒓𝒐𝒓 𝒂𝒄𝒄𝒆𝒑𝒕𝒆𝒅 𝒗𝒂𝒍𝒖𝒆 ×𝟏𝟎𝟎% %𝒆𝒓𝒓𝒐𝒓= |𝒆𝒙𝒑𝒆𝒓𝒊𝒎𝒆𝒏𝒕𝒂𝒍 𝒗𝒂𝒍𝒖𝒆 − 𝒂𝒄𝒄𝒆𝒑𝒕𝒆𝒅 𝒗𝒂𝒍𝒖𝒆| 𝒂𝒄𝒄𝒆𝒑𝒕𝒆𝒅 𝒗𝒂𝒍𝒖𝒆 ×𝟏𝟎𝟎%

Percent Composition You have a 100 g mixture of sugar and water. What is percent composition of sugar if there are 20 g of sugar in the mixture? Percent composition % 𝒔𝒖𝒃𝒔𝒕𝒂𝒏𝒄𝒆 = 𝒎𝒂𝒔𝒔 𝒐𝒇 𝒂 𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕 𝒕𝒐𝒕𝒂𝒍 𝒎𝒂𝒔𝒔 ×𝟏𝟎𝟎%

Measurement is a quantitative observation Measurement always has a number and a unit of measurement 2 dollars 2 cents 2 g 2 kg