Ch 5: Measurements and Calculations

I. Scientific Notation and Units Scientific Notation: A way to easily show lengthy numbers. M x 10n where 1 < M < 10 and n = decimals to move. Move decimal till number is between 1 and 10 Determine the exponent (n) Positive n = moved to the left Negative n – moved to the right 12 grams of carbon has 602,200,000,000,000,000,000,000 atoms in it. If a pile of carbon weighs 41 grams, how many carbon atoms are in the pile? The Sun is 93,000,000 miles away if you travelled 5000 miles per hour how many hours would it take to reach the sun? How many days would it take to reach the sun? How many years would it take to reach the sun? A different way to show a number 4.3 x 10 = 4.3 / 10 = 4.3 /10/10 = 4.3 /10/10/10 = 4.3 x 10 x 10 = 4.3 x 10 x 10 x10 = What’s the rule this shows? Every time you divide by 10 it moves the decimal to the left 1 spot What’s the rule this shows? Every time you multiply by 10 it moves the decimal to the right 1 spot.

Scientific Notation Practice Change the following to Scientific Notation 9314 0.08042 0.0000517 7,124,369,582 Change the following to standard numbers. 4.17 x 104 6.19 x 10 -2 3.001 x 10-5 5.91 x 10 7

Units: Indicator of what scale is used for measuring. International System of Measurement (SI) Mass = The quantity of matter in an object = Grams (g) Length = Meters (m) Time = Seconds (sec) Temperature = Kelvin (K) Volume = 3 dimensional space taken up = Liter (L) Use prefixes to make numbers usable (verbal multiplier)

Converting Metric Prefixes. Determine the difference between the exponent for each unit. Move the decimal that many places. If going down the table, move right. If going up the table move left. Convert The following 5.45kg  g 100 Base Unit -g -L -m µ 6.19nm  m 4.90 x 107 µL  kL 1.34 x 10-5 ML  L

II. Uncertainty in Measurments All measurements have an estimated digit. Determine the smallest digit that is indicated on the device, and estimate one digit farther.

Significant Figures: The numbers that were actually recorded in a measurement. Rules for counting Significant Figures: Nonzero’s are significant Final zero’s after the decimal are significant Zero’s that are between other significant figures are significant. How many significant figures are in each of the following numbers? 0.00240g 1.00240 1000L 1000.0L Pg 146 Example 5.3 a-d

Exact Numbers: numbers determined by counting. 1. have unlimited significant digits. Pg 146 Practice Problem Exercise 5.3 a-c

1. Addition or subtraction: Significant Figures in Calculations: (How many digits should I keep in my answer?) 1. Addition or subtraction: The answer may hold as many decimal places as the number from the problem that has the least decimal places. (round to that place value) 2. Multiplication or Division: The answer may hold as many significant figures as the number from the problem that has the least significant figures. (round to that number of significant figures. 12.11g + 18.0g + 1.013g = 31.123g 353.2mL + 17.89 mL= 371.09mL 183.062km – 14km = 169.062km Pg 149 Practice Problem Exercise 5.5 a-c 4.56 m x 1.4m = 6.384m2 8.315g / 298L = 0.0279027g/L Pg 150: 5-7 4.87m / 8.73g x 13m = 7.252 m2/g

How many sig. fig. should be in each result Results 5.4 c) 5.0 x 107 100 d) 88500 Number of sig. figs in a measurement. 2 (example is 14) 3 (example is 3.14) 2 (example is 4.6)

III. Problem Solving and Unit Conversions You need two dozen doughnuts for advisory groups. Dunkin Donuts sells doughnuts for $0.50 each. How much will the doughnuts cost? Problem Solving: Where do we want to go? What is the problem asking for? What do we know? List of facts. How do we get there? What steps can we take to solve the problem. Does it make sense? Evaluate if the answer is reasonable

Algebra Review 𝟏 𝟏 = 5 5 = 1.456 1.456 = 𝑥 𝑥 = What’s the rule? Anything divided by itself = 1

Algebra Review 5 • 1 = 17 • 1 = 1.456 • 1 = 1,346,000.309534 • 1 = x• 1 = What’s the rule? Anything multiplied by 1 stays the same.

Algebra Review 2𝑥 𝑥 = 4𝑥 2𝑥 = 6𝑥 1 • 2𝑦 𝑥 = 45x • 3𝑦 9𝑥 =

Converting Units of Measure: Changing the units of a measurement but keeping the value the same. Equivalence Statement: Shows two different #’s that are the same value. (2.45cm = 1 in.) See pg 153 Conversion Factors: A ratio that relates two units. They are made from the 2 parts of an equivalence statement. 2.54𝑐𝑚 1𝑖𝑛. or 1𝑖𝑛 2.54𝑐𝑚 A conversion factor allows us to cancel out a unit and replace it with new unit. Practice Problem 5.6 pg 156 You need two dozen doughnuts for advisory groups. Dunkin Donuts sells doughnuts for $0.50 each. How much will the doughnuts cost? (show using unit conversion)

How to use a conversion factor to do a conversion Use Table 5.7 to make the following conversion. Convert 3.79kg to lbs. Use Table 5.7 to make the following conversion. Convert 2.37mi to m. Use Table 5.7 to make the following conversion. Convert 35.7qt to L How to use a conversion factor to do a conversion Identify the equivalence statement(s) that will help with this problem. Write the number and unit given in the problem. Multiply by a conversion factor (fraction) where The bottom has the unit you want to get rid of. (so it cancels out) The top has the unit that you want to end up with. Do the appropriate math. Make sure you have the correct number of significant figures. (look at the original measurement to determine sig. figs.) Pg 170:2-4

Conversion Factors and metric Prefixes. 100 Base Unit -g -L -m µ 1 1 M__ 106 __ 1 k__ 103 __ 1 d__ 10-1 __ 1 c__ 10-2 __ 1 m__ 10-3 __ 1 µ__ 10-6 __ 1 n__ 10-9 __ = Convert 35mg to g Convert 7.38m to Mm Convert 41.9kL to dL

Temp. Conversions Celsius Scale: Based on the freezing and boiling point of water Tf = 0 oC Tb = 100oC Kelvin Scale: Base on absolute zero as the coldest temp. Tf = 273K Tb = 373K Conversions: C K add 273 to the celcius temperature. K  C subtract 273 from the kelvin temperature. Complete the following conversions -215o C to K 143o C to K 198K to o C 199K to o C

Density: The amount of matter present in a given volume of a substance. Mass per unit of volume ( 𝑔 𝑚𝐿 ) The density of a type of material is always the same. (ie. The density of copper is 8.92g/mL) D = 𝑚 𝑣 m = mass (g) D = Density, V = volume (mL or cm3 ) Use this equation to determine the density, mass, or volume of an object.

Density Problems The density of a piece of metal is 1.113g/mL. What is the volume of a piece of metal with a mass of 1.45kg? The density of a rock is 0.9980g/mL. What is the mass of the rock if the volume is 345mL? If a block of stone has a mass of 45.3g and takes up a volume of 100.4mL, what is its density?