How to express a number in terms of scientific notation: Examples: Consider the numbers 360,000 and :

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1 Chemistry Ms. Ye Name Date Block Scientific Notation: used to express or numbers more easily It is written as a ( ) X ex: 3.2 x 10 3, 7.2 x 10 4 How to express a number in terms of scientific notation: Examples: Consider the numbers 360,000 and : 1. Move the decimal point of your number so that you have a decimal between 1 and , *Note: if no decimal point is written, the decimal point is at the end of the number! 2. Count the number of spaces (n) and which direction you moved the decimal point 360, : 5 decimal places to the left : 4 decimal places to the right If you moved the decimal point to the left multiply (x) your decimal by 10 n: 360, x 10 5 If you moved the decimal point to the right, multiply (x) your decimal by 10 n: x 10 4 Practice: Write the following numbers in terms of scientific notation Category Normal Number Scientific Notation Population of the World 7,125,000,000 people Distance from the Earth to the Moon 240,000 miles Raindrops in a Thundercloud 6,000,000,000,000 drops Density of Oxygen g/cm 3 Mass of a Dust Particle kg

2 Chemistry Ms. Ye Name Date Block How to express a value given in scientific notation as a normal number: Examples: Consider the numbers 3.6 x 10 5 and 3.7 x 10 4 : 1. Identify the exponent 3.6 x 10 5 : exponent is x 10 4 : exponent 4 2. If the exponent is a positive number, move the decimal point the same number of places to the right. Fill in 0 s as placeholders as necessary. 3.6 x 10 5 : move decimal 5 places to the right: 3.6_._._._. 360, If the exponent is a negative number, move the decimal point the same number of places to the left. Fill in 0 s as placeholders as necessary. 3.7 x 10 4 : move decimal 4 places to the left:._._._ Practice: Write the following scientific notation expressions as a normal number Category Normal Number Scientific Notation Speed of Light 3.00 x 10 8 m/s Distance from the Earth to the Sun Cells in the Human Body Water on Earth s Surface Diameter of a Grain of Sand 9.3 x 10 7 miles 1.0 x cells 1.40 x 10 8 square miles 2.4 x 10-3 inches

3 Recall: Metric Prefixes Prefix Mega Kilo Hecto Symbol M k h Deca da Base (None) (None) Deci Centi Milli d c m Micro µ Helpful Mnemonic: Ms. Karen Heats Dollar Bills. Doesn t Chem Make μ Nervous? Prefixes at the of the chart represent a amount or quantity. Prefixes at the of the chart represent a amount or quantity. Nano n Dimensional Analysis (aka Factor-Label Method, Unit-Factor Method) Can be used to convert from one unit to another; it is based on the idea of cancelling out units! It is super important to WRITE OUT ALL UNITS when doing this! Ex: Convert 1609 meters into kilometers 1. Identify the quantity you re starting with, including the unit 2. Set up a conversion factor (fraction) so that you can cancel out a unit from the numerator with one in the denominator 3. Place a 1 in front of the larger unit 4. Determine the number of smaller units needed to make 1 of the larger unit 5. Cancel out similar units: a unit in the numerator cancels with one in the denominator if they are the same Multiply numbers that are in the numerator; divide this by the numbers that are in the denominator. Express your final answer with the proper unit = =. Final Answer: 1609 m = km Practice: Convert the following: 1) 950 g = kg 3) μm = nm 2) 35 ml = dl 4) MHz = khz

4 HOMEWORK Part 1: Convert the following numbers to scientific notation 1) ) ) 198,000,000 4) ) 3600 Part 2: Convert the following expressions to normal notation 6) 3.6 x ) 4.5 x ) 7.2 x ) 1.04 x ) x 10 3 Part 3: Perform the following metric conversions using the dimensional analysis technique. SHOW WORK! mm = cm kg = cg L = ml ml = L

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