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**Review of Essential Skills:**

SI Units, Scientific Notation, Significant Figures & Rounding

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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 (m3)

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

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**SN Recipe Place a decimal to get a number between 1 and 10.**

Multiply by 10. Add a power/exponent to the 10 based on the number of times you moved the decimal.

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**Eg.1: Convert each number below to scientific notation.**

Eg.2: Convert each number to real notation. a) km b) s = = = 6.73 x 10-2 km = x 108 s a) 4.5 x 103 m b) x 10-7 s = 45 00 = = m = s

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**Significant Figures (“Sig Figs”)**

Values that are significant to a measurement Gives certainty to any measure. Guidelines Count from left to right, beginning with the first non-zero digit. Number # of Significant Digits 345 3 457.35 5

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**2. Zeros at beginning are never significant.**

Number Sig Figs 0.235 3 0.003 1

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**3. All non-zero digits in a number are significant.**

Sig Figs 1.1223 5 76.2 3

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**4. Zeros between digits are significant.**

Number Sig Figs 107.05 5 4

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**5. Zeros at the end of a number with a decimal point are significant.**

Sig Figs 10.0 3 303.0 4

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**6. Zeros at the end of a number without a decimal are not significant.**

Sig Figs 5400 2 1

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**7. All digits in the coefficient of a number written in scientific notation are significant.**

Sig Figs 5.4 x 103 2 5.40 x 103 3 5.400 x 103 4

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**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 32000 m m 15000 m 100.0 m m 2 Last 3 zeros are placeholders 5 Last 2 zeros are placeholders ~ 4 Tilde (~) indicates last significant figure 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

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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.

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**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 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

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**Eg.5: 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.5: Consider the following data set: [1.5, 2.5, 3.5, 4.5] Original sum: = 12 Rounding Rule for 0.5 Rounded Set Sum Round up “5 Rule” [2,3,4,5] 14 [2,2,4,4] 12

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