Math Unit The metric system, scientific notation, factor labeling and problem solving

3 Warm-up Question Liberia Myanmar (formerly Burma) The United States is one of how many countries in the world that still use the imperial system of measurement? What are the other countries? 3 Liberia Myanmar (formerly Burma)

Units of Measurement SI Units a system of units of measurements devised around seven base units and the convenience of the number ten.

Units of Measurement Metric System

Units of Measurement

Sample problem Convert the following Start with 53. Move the decimal to the right Move the decimal to the left Convert the following 53 hg = ________dg Start with 53. Move the decimal 3 spaces to the right 53 Fill in the empty spaces with zeros 53000 dg

Sample Problem Start with 300. Move the decimal to the right Move the decimal to the left Convert the following 300 cg = ________kg Start with 300. Move the decimal 5 spaces to the left 300 Fill in the empty spaces with zeros 0.00300 kg

Units of Measurement Examples… 1000 mg =__________ g 160 cm = __________ mm 109 g = __________ kg 1 L = __________ mL 14 km = __________ m 1 1600 0.109 1000 14000 Move the decimal to the right Move the decimal to the left

Exit Question Now that you are a metric master, would it be easier to convert inches to miles or centimeters to kilometer? Explain.

602000000000000000000000 Warm-up Question It’s a mole!!! What is the significance of this number? 602000000000000000000000 It’s a mole!!! (the SI unit for a amount of a substance)

Scientific Notation Scientific notation expresses numbers as a multiple of two factors: a number between 1 and 10 (coefficient); and ten raised to a power, or exponent. The exponent tells you how many times the first factor must be multiplied by 10. When numbers larger than 1 are expressed in scientific notation, the power of 10 is positive. When numbers smaller than 1 are expressed in scientific notation, the power of 10 is negative. Exponent 6.02 𝑥 10 23 Coefficient

Scientific Notation Examples… Change the following data into scientific notation: The diameter of the Sun is 1,392,000 km. The density of the Sun’s lower atmosphere is 0.000000028 g/cm3. 1.392 𝑥 10 6 km 2.8 𝑥 10 −8 g/cm3

Scientific Notation Adding and Subtracting Using Scientific Notation The exponents must be the same before doing the arithmetic. Convert the smaller number to the bigger one, by moving the decimal to the right. Add or subtract the coefficient. Keep the exponent the same. Make sure your answer is written in proper scientific notation. Example… 1.26x104 kg + 2.5x103 kg = ____________________ kg 1.51x 104

Scientific Notation Multiplying and Dividing Using Scientific Notation Multiply or divide the coefficients. Add the exponents (for multiplication) or subtract the exponents (for division). Examples… (2x103 cm) x (3x102 cm) = ____________________ cm2 (9x108 g) ÷ (3x10-4 mL) = ____________________ g/mL 6 x 105 3 x 1012

Exit Question Scientific notation should come in handy when expressing what kinds of quantities in chemistry? Submicroscopic things like the size of an atom or the number of atoms in a substance.

Warm-up Question How can you simplify this problem before you calculate the answer? 2 5 × 3 4 =

Dimensional Analysis (Factor Label) A conversion factor is a ratio of equivalent values used to express the same quantity in different units. A conversion factor is always equal to 1. 100 𝑐𝑚 1 𝑚 = 1 𝑚 100 𝑐𝑚 = 1 Dimensional analysis is a method of problem-solving that focuses on the units used to describe matter. Dimensional analysis often uses conversion factors. When you convert from a large unit to a small unit, the value of the number must increase. When you convert from a small unit to a large unit, the value of the number must decrease.

Factor Label Method of Conversion 100 cm = 1 m 1 m = 100 cm Use conversion factors to systematically move from one unit to the next, cancelling out units on the diagonal in each step. Convert 18 m = _______ cm 100 cm 18m = 1800 cm 1 m

Dimensional Analysis 24 hr 90 km 60min 60sec = 86400 sec 1 hr 1 min Examples… How many seconds are there in 24 hours? A car is traveling 90.0 kilometers per hour. What is its speed in miles per minute? 60min 60sec 24 hr = 86400 sec 1 hr 1 min 90 km 1 hr 0.62mi 1 hr = 0.93 mi/min 1 km 60 min 1 km = 0.62 miles 1 hr = 60 mins 1 min = 60 secs

Exit Question How many fuggles are there in 19 blops? On the planet Rigel, Rigellians have developed a system of measurements called S.U., or Systems Universal. Here is the conversion table for the measurements of distance:   1 gleem = 27 blops 1 blop = 34 riddigs 1 riddig = 42 chirks 1 chirk = 9 fuggles 10 fuggles = 52 hippers 2.5 hippers = 1.2 zookas 1 zooka = 7 wenzels Use the Factor Label Method and the conversions above to solve the problem. How many fuggles are there in 19 blops?  

Problem Solving It is important to understand what you have, what you need and how you are going to get it. Example The mass of a brick of aluminum is 87 g. If the density of aluminum is 2.7 g/ml, what is the volume of the brick? Have Need How Mass=87g Volume V=M/D Density = 2.7 g/mL D=M/V