Scientific Measurement Chapter 3 Scientific Measurement

3.1 The importance of Measurement Not all measurements give the same amount of information! Qualitative measurements: give descriptive, non-numerical results (NO NUMBERS) Think ‘quality’ Quantitative: give results with numbers and units (NUMBERS! Think ‘quantity’. Quantity means numbers

Scientific notation Scientific Notation: number is written as the product of two numbers: a number greater than or equal one and less than 10 and a power of 10. ex: 1,200 = 1.200 x 103

How to write in scientific notation 1. Write the number you are starting with 2. Move the decimal behind the first digit in the number Write ‘x 10’ Count the ‘jumps’ this is the ‘power of 10’ 3. Decide if the new number is bigger or smaller than the old number Bigger = negative jumps Smaller = positive jumps

Let’s try it! 1,230, 900 Write the number: 1,230,900.00 Move the decimal: 1.230900 Write x 10: 1.230900 x 10 Count the jumps: 6 jumps Is the new number bigger or smaller than the old number? Smaller = positive jumps! 1.230900 x 10 6

Let’s try another! 0.000045672 1. Write the number: 0.000045672 2. move the decimal: 4.5672 3. write ‘x 10’: 4.5672 x 10 4. count the jumps: 5 jumps 5. is the new number bigger or smaller than the old number: Bigger = Negative! 4.5672 x 10 -5

How to write in standard form Standard form= this is just the regular way to write numbers Look at the exponent (number on the x 10). If it is positive, make the number bigger. If it is negative, make the number smaller. Count the jumps Place new decimal

Let’s try it! 3.567 x 103 1. Look at the exponent: it is positive, so we have to make the number BIGGER 2. count the jumps: 3 jumps 3. place the new decimal 3,567 is the standard form

Let’s try another! 5.6374 x 10 -6 Look at the exponent = negative: make number smaller! 2. count the jumps = 6 jumps 3. place new decimal 0.0000056374

You try it! Write the following numbers in scientific notation: 1. 3,567,987 2. 0.0007634 3. 0.5553211 4. 124.00 5. 6 6. 12,000 7. 0.00000000004

More Practice! Write the following numbers in standard form 1. 1.745 x 106 2. 3.20012 x 103 3. 8.972 x 10-2 4. 6.788822 x 10-8 5. 2.221 x 10 10 6. 7.700123 x 10 -10

You try it! pg 53: 1-3 Pg 78: 36, 67, 79-83

Plug it in your calculator! To enter a number in scientific method on a calculator: 1. Do you have a light blue or a dark blue calculator? DARK BLUE: Type in digit: ex. 1.2345 Hit the ‘2nd button’(light blue button, upper left) Hit the ‘x-1’ button (above the ‘7’) Your calculator should read ‘1.2345 E’ Enter exponent (power of 10)

Light Blue: Type in digit: ex. 1.2345 Hit ‘EE button’ (above ‘7’) Your calculator should read 1.2345 E Type in exponent (power of 10)

Now you can do operations with exponents! Let’s try it! 1.234x103 + 2.3456x108 = 3.23x10-4 – 9.1x1014= 6.367x1023 x 7.67x108 = 2.112x1019 / 6.778x10-2=

Today’s challenge 1. Get into pairs 2. Design a 20 question quiz for scientific notation. Can include operations, word problems, identification, whatever! Include answer key Best quiz? Becomes CLASS quiz! WINNERS EXEMPT AND GET 100%!!!!

3.2 Accuracy in Measurements Accuracy: a measure of how close a measurement comes to the actual value Precision: a measure of how close a series of measurements are to one another Error = experiemental value – accepted value Percent error = |error|/accepted value x 100

Significant Figures in measurements Significant figures: all of the digits that are known, plus the last digit which is estimated. Think of 3 different rulers: One broken into whole meters One broken into decimeters One broken into centimeters Which is more precise? WHY?

You try it: Count the number of sig figs in each measurement 1. 1,000.089 2. 19 birds in a tree 3. 0.00071 4. 23,013.00 5. 8,000,000 6. 303 7. 303.00 9. 00303.00 10. 303030.00

ROUNDING! When completing measurements in a lab setting, you must ROUND to the appropriate number of SIG FIGS! 1. underline the place value you are rounding to (nearest tenth, etc) Draw an arrow to the digit behind that place value 3. ask yourself: “5 or above? Give it a shove” “4 or below? Leave it alone!”

You try it: Round to the nearest tenth Round to the nearest hundredth Round to the nearest whole number 1. 12.35467 2. 673.000233333 3. 0.8999 4. 0.0123

Reading Instruments In a lab, you will have to read instruments to the appropriate number of sig figs. 1. Read the instrument all the way 2. Estimate last digit (this is uncertain) Ex. If your ruler goes to centimeters, your measurement will go to tenths of a centimeter 2.4 centimeters (the .4 centimeters is estimated)

More Practice: Pg 58, # 5 and 6 Worksheet Due at end of period

Today’s Challenge: Get into Pairs Each of you separately mark a measurement on the blank sheets Swap papers Complete independently Swap back and grade How did you do? Hand them in 

Wrap up! On a sheet of paper (to be collected by the end of period) 1. What are significant figures? 2. Why do we count them? 3. How do we read a measuring device to the appropriate number of significant figures? 4. What is different about the last digit of a measurement? Pg 78: # 36-43

Significant figures in calculations Addition and Subtraction: round to the same number of DECIMAL PLACES as the number with the LEAST number of decimal places Multiplication and Division: round to the same number of SIGNIFICANT FIGURES and the number with the LEAST number of significant figures

Let’s try it: 61.2 meters + 9.35 meters + 8.6 meters = LOWEST NUMBER OF DECIMAL PLACES? 61.2 OR 8.6 HAS ONE DECIMAL PLACE. ANSWER WILL BE ROUNDED TO ONE DECIMAL PLACE!!! 7.55 meters x 0.34 meter = LOWEST NUMBER OF SIG FIGS? 0.34 HAS 2 SIG FIGS. ANSWER WILL HAVE 2 SIG FIGS!!

More Practice: 9.44 meters – 2.11 meters = 8.3 meters x 2.22 meters = 8432 meters / 12.5 = 35.2 seconds / 60 =

Today’s Challenge! Get into pairs Write a 20 question quiz on ONLY significant figures Your quiz should include counting sig figs, rounding to the right number of sig figs, and calculations with sig figs You must include an answer key Winners receive 100% on quiz and are exempt tomorrow!

International System of Units International system of units (SI)= revision of the metric system. Every unit is a multiple of 10. This makes converting from one unit to another EASY!

Units of Measurement Length meter Volume cubic meter or liter Mass kilogram Density grams/cm3 Temperature kelvin or degrees Celsius Time second Pressure pascal or atmosphere Energy joule

Prefixes Prefixes are used to tell you how many multiples of 10 something is. Sometimes the SI unit isn’t a practical measurement. For example: meters to measure the size of an atom. Atoms are way too small to be measured in meters, it’s not practical! We use a smaller multiple of meters and denote it with a prefix (nanometers)

Volume Volume: the space occupied by a sample of matter SI unit is milliliter or cubic centimeter We often use liter to measure volume WHY???

Mass Mass: the amount of matter in an object Weight: measure of the pull of gravity on an object Weight can change with location, mass can’t SI unit = Kilogram Kilo=1000 We often use grams in lab. WHY????

Density Which is heavier, a pound of lead or a pound of feathers? What’s the difference between the two quantities? DENSITY!

Generally, density decreases as temperature increases. Density = mass/volume Matter with a lower density will float on matter with a higher density (liquids and gases) Generally, density decreases as temperature increases. water is most dense at 4 degrees Celsius What happens with ice on water? What can you assume about the density of ice? What happens when you fill a balloon with helium? What can you assume about the density of helium?

Specific Gravity Specific Gravity: comparison of the density of an object to the density of water. Specific gravity = density of object/density of water Hydrometer: device used to measure the specific gravity of a liquid Why do you think this comparison is made to WATER????

Practice! Pg 67, 17-22 Pg 71, 23-24 Pg 72, 25-29

Dimensional Analysis You must be able to convert from one unit to another. This skill will be used for the REST OF YOUR LIFE!!!! 1. start with what you know 2. write conversion factor as a fraction 3. what you want goes on top! 4. multiply or divide as necessary

Common Conversion factors 1 kilometer = 1,000 meters 1 centimeter = .01 meters 1 millimeter = .001 meters 1 hour = 60 minutes 1 yard = 3 feet 1 mole = 6.02 x 1023 particles

Let’s try one 273 meters to kilometers 1. start with what you know 2. Write conversion factor as a fraction 1 km = 1000 meters 1km/ 1000meters 3. What you want goes on top! I want to end with kilometers, so it goes on top! 4. Multiply or divide as necessary 273 meters x 1 km/ 1000 m = 0.273 km

Let’s try some more! Convert to meters: 267 cm 273 mm 273 km Convert to hours 273 minute Convert to yards 273 feet