COS 12.0 IDENTIFY METRIC UNITS FOR MASS, DISTANCE, TIME, TEMPERATURE, VELOCITY, ACCELERATION, DENSITY, FORCE, ENERGY & POWER
WHAT YOU’LL LEARN Name the prefixes used in SI & indicate what multiple of ten each one represents. Identify SI units and symbols for mass, length (distance), time, temperature, velocity, acceleration, density, force, energy & power. Convert related SI units. Use scientific notation & significant figures in problem solving. Identify the significant figures in calculations. Understand the difference between precision & accuracy
UNITS OF MEASUREMENT What is a measurement? A measurement is a number and a unit. 14.5 meters, 35 dozen, and 1 hour are all measurements.
Significant figure prescribed decimal place that determines the amount of rounding off to be done based on the precision of the measurement Precision exactness of a measurement Accuracy description of how close a measurement is to the true value of the quantity measured
Rules For Significant Digits Digits from 1-9 are always significant. Zeros between two other significant digits are always significant One or more additional zeros to the right of both the decimal place and another significant digit are significant. Zeros used solely for spacing the decimal point (placeholders) are not significant.
EXAMPLES OF SIGNIFICANT DIGITS EXAMPLES# OF SIG. DIG.COMMENT 453 kg3 All non-zero digits are always significant. 5057 L4 Zeros between 2 sig. dig. are significant. 5.003 Additional zeros to the right of decimal and a sig. dig. are significant. 0.0071 Placeholders are not sig.
Multiplying and Dividing RULE: When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits.RULE: When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits. Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525 cm 3Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525 cm 3 We look to the original problem and check the number of significant digits in each of the original measurements:We look to the original problem and check the number of significant digits in each of the original measurements: 22.37 shows 4 significant digits.22.37 shows 4 significant digits. 3.10 shows 3 significant digits.3.10 shows 3 significant digits. 85.75 shows 4 significant digits.85.75 shows 4 significant digits. Our answer can only show 3 significant digits because that is the least number of significant digits in the original problem.Our answer can only show 3 significant digits because that is the least number of significant digits in the original problem. 5946.50525 shows 9 significant digits, we must round to the tens place in order to show only 3 significant digits. Our final answer becomes 5950 cm 3.5946.50525 shows 9 significant digits, we must round to the tens place in order to show only 3 significant digits. Our final answer becomes 5950 cm 3.
Adding and Subtracting RULE: When adding or subtracting your answer can only show as many decimal places as the measurement having the fewest number of decimal places.RULE: When adding or subtracting your answer can only show as many decimal places as the measurement having the fewest number of decimal places. Example: When we add 3.76 g + 14.83 g + 2.1 g = 20.69 gExample: When we add 3.76 g + 14.83 g + 2.1 g = 20.69 g We look to the original problem to see the number of decimal places shown in each of the original measurements. 2.1 shows the least number of decimal places.We look to the original problem to see the number of decimal places shown in each of the original measurements. 2.1 shows the least number of decimal places. We must round our answer, 20.69, to one decimal place (the tenth place).We must round our answer, 20.69, to one decimal place (the tenth place). Our final answer is 20.7 gOur final answer is 20.7 g
Scientific Notation The number 123,000,000,000 in scientific notation is written as : 1.23 x 10 11 The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and less than 10. The second number is called the base. It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x 10 11 the number 11 is referred to as the exponent or power of ten.
Scientific Notation To write a number in scientific notation: Put decimal after first digit and drop zeroes. 1.23000000000 In number 123,000,000,000 coefficient will be 1.23 To find exponent count number of places from decimal to the end of number. In 123,000,000,000 there are 11 places. Therefore we write 123,000,000,000 as: 1.23 x 10 11
Scientific Notation For small numbers we use a similar approach. Numbers smaller than 1 will have a negative exponent. A millionth of a second (.000001) is: 1.0 x 10 -6
Standard Form Is just opposite of scientific notation! 6.33 X 10 8 = 633,000,000 All we’ve done is moved decimal eight (8) places to right. 5.18 X 10 -7 =.000000518 All we’ve done is moved decimal seven (7) places to left. IT’S THAT EASY!
Write the following in scientific notation: 4,100,000 = _______________ 345,600,000,000 = _________ 0.0456= ________________ 0.00000012=____________ 0.00305= ____________ 4.1 x 10 6 3.456 x 10 11 4.56 x 10 -2 1.2 x 10 -7 3.05 x 10 -3
Write the following in standard form: 4.67 x 10 3 =__________________ 3.112 x 10 5 = _________________ 3.112 x 10 -4 = ________________ 4 x 10 -6 = ___________________ 1 x 10 11 = __________________ 4670 311200 0.0003112 0.000004 100,000,000,000
WHY SI UNITS? metric standard of measurement (for most nations) each type of SI measurement has a base unit base unit fundamental unit of measurement which are used to form other, compound units for other quantities. (SI base unit)
What does SI stand for? international system of units
SI PREFIXES Easy to use because it is based on multiples of ten.
PrefixSymbolMultiplying factor gigaG1000000000 or 10 9 megaM1000000 or 10 6 kilok1000 or 10 3 hectoh100 or 10 2 dekada (dk)10 or 10 1 Base unit0 decidc.1 or 10 -1 centic.01 or 10 -2 millim.001 or 10 -3 microµ.000001 or 10 -6 nanon.000000001 or 10 -9
K H D O D C M Changing from one metric unit to another is called metric conversion “M” is the space where meter, liter, or gram belongs or base unit (0) Let’s practice! To change from one metric unit to another, we simply move the decimal point. For example: 25.4 km = ? cm K-H-D-O-D-C is 5 places to the right 25.4 km = 2,540,000 cm
K H D O D C M 30 cm = ? hm C – D- O –D- H is 4 places to the left 30 cm = 0.0030 hm (this is the same as 0.003 hm) 14 dal = _____dl D- O –D is 2 places to the right 14 dal = 1400 dl Find the difference between the exponents of the two prefixes. Move the decimal that many places.
SI Prefix Conversions 20 cm = _______m 0.032 A = _______ mA 45 m = _______ nm 805 dm = _________ km 0.2 0.0805 45,000 32