Review of Essential Skills: Scientific Notation, Significant Figures & Conversions

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: Standard unit for time Some examples: Speed (m/s), Volume (m3)

Scientific Notation Often in Physics, calculations require the usage of large figures, scientific notation makes these calculations easier. Some examples: 37010000 m = 3.701 x 107 m 0.00003152 s = 3.152 x 10-5 s Decimal moved left? Positive Exponent Decimal moved right? Negative Exponent

Significant Figures (“Sig Figs”) Values that are significant to a measurement. Some examples: Value # of Sig Figs Comment 32000 m 2 Last 3 zeros are place holders 1201500 m 5 Last 2 zeros are place holders 15000 m 4 Tilde (~) implies answer accurate to tens (dm) 100.0 m 0.0013200 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. In General: Leading / trailing zeros are typically placeholders, not part of the measurement itself.

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.1: 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 5.637 3 4.6337 3.65 2 3.55 3.5500 3.651 5.64 4.63 3.6 3.6 3.6 3.7

Eg.2: Consider the following data set: [1.5, 2.5, 3.5, 4.5] Why the “5 rule”? Automatically rounding up skews data in one direction. Eg.2: Consider the following data set: [1.5, 2.5, 3.5, 4.5] Original sum: 1.5+2.5+3.5+4.5 = 12 Rounding Rule for 0.5 Rounded Set Sum Round up “5 Rule” [2,3,4,5] 14 [2,2,4,4] 12

Conversions Done by a process called “multiplication by ones”. Unwanted units cancel. Eg.3: Convert 72 km/h to m/s * One unit at a time

Eg.4: Convert 5 kg/m2 to g / km2