SI Units, Scientific Notation, Significant Figures & Rounding
SI Units Standard Unit: Metric is usually the preferred unit in science. Metric referred to as “S.I.” (System Internationale) Also known as MKS system Metres: Standard unit for distance Kilograms: Standard unit for mass Seconds: Stanard unit for time Some examples: Speed (m/s), Volume (m 3 )
Scientific Notation Often in Physics, calculations require the usage of large figures, scientific notation makes these calculations easier. Some examples: m = x 10 7 m s = x s Decimal moved left? Positive Exponent Decimal moved right? Negative Exponent
SN Recipe 1. Place a decimal to get a number between 1 and Multiply by Add a power/exponent to the 10 based on the number of times you moved the decimal.
Eg.1: Convert each number below to scientific notation. Eg.2: Convert each number to real notation. = x 10 8 s a) kmb) s = = 6.73 x km = a) 4.5 x 10 3 mb) x s = = m = = s
Significant Figures (“Sig Figs”) Values that are significant to a measurement Gives certainty to any measure. Guidelines 1. Count from left to right, beginning with the first non-zero digit. Number# of Significant Digits
2. Zeros at beginning are never significant. NumberSig Figs
3. All non-zero digits in a number are significant. NumberSig Figs
4. Zeros between digits are significant. NumberSig Figs
5. Zeros at the end of a number with a decimal point are significant. NumberSig Figs
6. Zeros at the end of a number without a decimal are not significant. NumberSig Figs
7. All digits in the coefficient of a number written in scientific notation are significant. NumberSig Figs 5.4 x x x
Significant Figures (“Sig Figs”) Values that are significant to a measurement. Leading / trailing zeros are typically placeholders. Eg.3: State the number of sig figs in each case. Value # of Sig Figs Comment m m m m m ~ Numbers recorded AFTER decimal place wouldn’t be recorded unless significant 4 5 Leading zeros not significant, last two digits are part of the measurement Last 3 zeros are placeholders Last 2 zeros are placeholders Tilde (~) indicates last significant figure
Rounding Rules Very simple set of rules with the exception of numbers terminating in 5 Rules: Number terminates in value > 5: Round up Number terminates in value < 5: Round down Number terminates in 5: Round to ensure the rounded value is an even number.
Eg.4: Round to the specific number of sig figs. Since the last example is terminated by a non-zero number, the “5 rule” does not apply… Value Sig Figs to Round To Answer
Why the “5 rule”? Automatically rounding up skews data in one direction. Eg.5: Consider the following data set: [1.5, 2.5, 3.5, 4.5] Original sum: = 12 Rounding Rule for 0.5 Rounded SetSum Round up “5 Rule” [2,3,4,5] [2,2,4,4] 14 12