Measurements and Calculations Chapter 2 Measurements and Calculations

Measurements Numbers Must consist a number and units E.g Quantitative observations Must consist a number and units E.g

2.1 Scientific Notation To show how very large or very small numbers can be expressed as the product of a number between 1 and 10 and a power of 10 Negative power = small value Moving the decimal point to the right 0.000035 => 3.5 x 10-5 Positive power = large value Moving the decimal point to the left 3568 = 3.568 x 103

2.1 Scientific Notation Express the following numbers in scientific notation 238,000 1,500,000 0.104 0.00000072

2.2 Units Part of measurement Unit system Require common units English system Metric system or International system (SI)

Table 2.1 Some Fundamental SI units Physical Quantity Name of unit Abbreviation Mass kilogram kg Length meter m Time second s temperature Kelvin K

Table 2.2 The Common Used Prefixes in the Metric System Symbol Meaning Scientific Notation mega M 1,000,000 106 kilo k 1,000 103 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

2.3 Measurements of Length, Volume and Mass meter Volume cm3 or ml Mass kg Weigh

2.3 Measurements of Length, Volume and Mass Consider the following objects then provide an appropriate measurement to each object 2.0 L 45.0 g 200 km 42.0 cm3

2.4 Uncertainty in Measurement Person Result of Measurement 1 2.85 cm 2 2.84 cm 3 2.86 cm 4 5

2.4 Uncertainty Every measurement has some degree of uncertainty The first digit is the certain digit The last digit in the measurement is the uncertain digit Determined by “guessing”

2.4 Uncertainty Determine the uncertain digit (estimate digit) in the following examples 2.54 60.028 1500 0.0078

2.5 Significant Figures Rules Nonzero integers are always significant 1, 2, 3 …… Leading zeros are never significant 0.078 => 2 s.f Captive zeros are always significant 103 => 3 s.f Trailing zeros at the right end of number are significant 2.30 => 3 s.f Exact number or counting number are never significant 2 books => none or indefinite

2.5 Significant Figures Determine the significant figures in each of the following measurements A sample of an orange contains 0.0180 g of vitamin C A forensic chemist in a crime lab weighs a single hair and records its mass as 0.0050060 g The volume of soda remaining in a can after a spill is 0.09020 L There are 30 students enrolled in the class

Activity (2.1 -2.4) What is the SI unit for time? What is the prefix for k? What does it mean? When do you use cm3? What is the difference between mass and weigh?

Activity (2.1 -2.4) Determine the significant figures and the uncertain digit in the following measurements: 2.56 cm 10.3 g 0.006 L 15 roses 0.07800 lb

2.5 Round Off Numbers Rules for Rounding Off If the digit to be removed is less than 5, the preceding digit stays the same 3.13 (3 s.f) => 3.1 (2 s.f) is equal to or greater than 5, the preceding digit is increased by 1 6.35 (3 s.f) => 6.4 6.36 (3 s.f) => 6.4 In a series of calculations, carry the extra digits through to the final result and then round off

2.5 – Determining Significant Figures in Calculation Multiplication and Division Report answer with the least number of significant figures E.g 4.56 x 1.4 = 6.384 = 6.4 8.315 ÷ 298. = 0.027903 = 0.0279 Addition and Subtraction Report answer with the least number of decimal places E.g 12.11 + 18.0 = 30.11 = 30.1 0.678 – 0.1 = 0.578 = 0.6

Examples Without performing the calculations, tell how many significant figures each answer should contain 5.19 + 1.9 + 0.842 = 1081 – 7.25 = 2.3 x 3.14 = The total cost of 3 boxes of candy at $2.50 a box

Examples Carry out the following mathematical operations and give each result to the correct number of significant figures 5.18 x 0.0280 = 116.8 – 0.33 = (3.60 x 10-3) x (8.123) ÷ 4.3 = (1.33 x 2.8) + 8.41 =

2.6 Problem Solving and Dimensional Analysis Also known as unit factor or factor-label method First, determined the units of the answer Second, multiply (or divide) conversion factor so that units are not need in the answer are cancelled out and units needed in the answer appear appropriately in either the numerator or denominator of the answer. Check for correct significant figures Ask whether your answer makes sense

Equality and Conversion Factors Equality = equivalent (English metric to English-English) 2.54 cm = 1 in 1 m = 1.094 yd 1 kg = 2.205 lb 453.6 g = 1lb 1L = 1.06 qt 1ft3 = 28.32 L Conversion Factor

Conversion Factors: One Step Problems An Italian bicycle has its frame size given as 62 cm. What is the frame size in inches? A new baby weighs 7.8 lb. What is its mass in kilograms? A bottle of soda contain 2.0 L. What is its volume in quarts?

Conversion Factors: Multiple – Step Problems The length of the marathon race is approximate 26.2 mi. What is this distance in kilometer? How many seconds in one day? You car has a 5.00-L engine. What is the size of this engine in cubic inches?

Freezing Point / Boiling

Boiling Point

2.7 Temperature Conversion Celsius to Kelvin TK = ToC + 273 Kelvin to Celsius ToC = TK -273 Celsius to Fahrenheit ToF = 1.80 (ToC) + 32 Fahrenheit to Kelvin ToC = ToF - 32 1.80

Example If your body temperature is 312 K, what is it on the Celsius scale? You’re traveling in a metric county and get sick. You temperature is 39oC. What is it on the Fahrenheit scale? Pork is considered to be well done when its internal temperature reaches 160.oF. What is it on the Celsius scale?

2.8 Density Defined as the amount of matter present in a given volume of substance. If each ball has the same mass, which box would weigh more? Why?

Examples A block has a volume of 25.3 cm3. Its mass is 21.7g . Calculate the density of the block. A student fills a graduated cylinder to 25.0 mL with liquid. She then immerse a solid in the liquid. The volume of the liquid rises to 33.9 ml. The mass of the solid is 63.5g. What is its density?

Examples Isopropyl alcohol has a density of 0.785 g/ml. What volume should be measured to obtain 20.0 g of liquid? A beaker contains 725 mL of water. The density of water is 1.00 g/mL. Calculate the volume of water in liters. Find the mass of the water in ounces.