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SNC2D SCIENTIFIC NOTATION,SIGNIFICANT DIGITS,& METRIC CONVERSIONS
SCIENTIFIC NOTATION • Scientists often have to work with very large or very small numbers. • It’s a system that uses a simpler form of these numbers. • In scientific notation, all numbers are written in the form: a x 10n • In this form, a can be greater than or equal to 1 but less than 10 and ncan be any value.
SCIENTIFIC NOTATION • For large numbers, move the decimal place to the left. • The number of times you move the decimal point to the left will be equal to the exponent on the base 10. • Example: 1500 (the exponent will be +3) 1.5 x 103 • For small numbers, move the decimal place to the right. • Note, the exponent on the base is negative. • Example: 0.0505 (the exponent will be -2) 5.05 x 10-2
SCIENTIFIC NOTATION • On a scientific calculator, enter using the following sequence: 5 . 0 5 EXP or EE +/- 2 • Practice converting the numbers below from standard form into scientific notation 8,200,000 = ______________________ 50,880,000,000,000 = ______________ 0.00012 = ________________________ 0.00000000458 = __________________ 8.2 x 106 5.088 x 1013 1.2 x 10-4 4.58 x 10-9
QUESTION • What is the length of the screw?
QUESTION • NOW ... what is the length of the screw? A ruler marked in millimeters can generally make a much more precise measurement than a ruler marked in centimeters.
SIGNIFICANT DIGITS • Every experiment involves some uncertainty in measurement. • Significant digits are CERTAIN digits (considered accurate) plus one UNCERTAIN (estimated) digit used in the measurement. • For example, the length of the screw: 5.N Vs 5.1N The precision of a measurement can be shown by the number of significant digits in the value.
SIGNIFICANT DIGITS RULES & EXAMPLES • Any non-zero digit is significant. • Ex. 227.4 has four significant digits. • Zeros used to space a number to the right of a decimal point are notsignificant. • Leading zeros are not significant (to the left of non-zero digits) • Ex. 0.000147has only three significant digits. • Trailing zeros, to the right of any non-zero digits, are not significant (when there is no decimal). • Ex. 74,000 has only two significant digits. • All other zeros are significant. • Ex. 60.59 has 4 significant digits.
CALCULATING WITH SIGNIFICANT DIGITS ROUNDING RULE: • Rounding after the last significant digit • < 5 ... Leave it • > 5 ... Round up • = 5 ... Round to the even number • Example: round numbers to 4 significant figures • 12.364 • 12.366 • 12.365 • 12.3649 • 12.36501 12.36 12.37 12.36 12.36 12.37
CALCULATING WITH SIGNIFICANT DIGITS RULE: • In any calculation, the number of significant digits in the answer cannot be greater than the number of significant digits of any measured value. • For example, suppose you do the following calculation: 5.73 x 2.1 = 12.033 • In this situation, the second measurement has the fewest significant digits. Therefore, the answer must also have just two significant digits and should be reported as 12.
CERTAINTY RULE FORMULTIPLICATION & DIVISION RULE: • The answer has the same number of digits as the least significant figure (regardless of placement). • Ex. 77.3 x 0.56 = • Ex. 2.541 x 4.01 = • Ex. 539.7 / 40. = 43.288 = 43 10.18941 = 10.2 13.4925 = 13
PRECISION RULE FORADDITION & SUBTRACTION RULE: • The answer has the same number of decimal places as the least number in the question. • Ex. 187.6 + 54.321 = 241.921 = 241.9
METRIC CONVERSIONS Metric system: • The system of units used by most scientists. • Also known as System International (SI) units. • In the metric system, different units for the same quantity are related to one another by prefixes. • Each prefix represents a multiple of 10.
METRIC CONVERSIONS • All the conversions are multiples of 10. • Converting from one unit to another, such as from meters to centimeters, simply involves shifting the decimal point to the left or right. Example: 12.56 meters = 1,256 centimeters = 0.01256 kilometers. • Follow the diagram in the handout.
METRIC CONVERSIONS Tips for solving unit conversion problems: • Always be aware of the unit you start with and the unit you have been asked for. • When converting any type of measures: • To convert from a larger to smaller metric unit you always multiply • To convert from a smaller to larger unit you always divide
METRIC CONVERSIONS • This is the metric conversion stair chart. You basically take a place value chart turn it sideways and expand it so it looks like stairs. • The Latin prefixes literally mean the number indicated. Meter, liter or gram can be used interchangeably.