Units and Conversions

PSSA PREP:Compared to the charge and mass of a proton, an electron has:

A.the same charge and a smaller mass

B.the same charge and the same mass

C.an opposite charge and a smaller mass

D.an opposite charge and the same mass

Units and Conversions

What will be covered:SI UnitsMetric Prefixes and Order of MagnitudeFactor-label conversionsMulti-dimensional conversionsHow will it be tested:The contents of this section will be embedded in EVERYTHING we do this year. I will always take off points for incorrect or lack of units and poor conversions. It is very important that we get these skills down right away, as they will erode our grades if we dont.SI UnitsInternational System of UnitsSI (French: Le Systme international d'units)

The modern form of the metric system.

SI is NOT a static set of units

The United States and the United Kingdom are pretty much the only two countries that do not wholly and singly acknowledge this system.SI Units : LengthThe Meter (m)Historically, the metre was defined by the French Academy of Sciences as the length between two marks on a platinum-iridium bar, which was designed to represent 1/10,000,000 of the distance from the equator to the north pole through Paris.

Today, it is defined by the International Bureau of Weights and Measures as the distance travelled by light in absolute vacuum in 1/299,792,458 of a second. SI Units:MassThe Kilogram (kg)It is defined as being equal to the mass of the International Prototype Kilogram. It is the only SI base unit with an SI prefix as part of its name. It is also the only SI unit that is still defined in relation to an artifact rather than to a fundamental physical property that can be reproduced in different laboratories. The mass of the kilogram is almost exactly equal to that of one liter of water. SI Units: TimeThe Second (s)The second is currently defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at absolute zero.SI Units: TemperatureThe Kelvin (K)The definition of the kelvin has three parts:It fixes the magnitude of the kelvin unit as being precisely 1 part in 273.16 parts the difference between absolute zero and the triple point of water; It establishes that one kelvin has precisely the same magnitude as a one-degree increment on the Celsius scale; and It establishes the difference between the two scales null points as being precisely 273.15 kelvins (0K= 273.15C and 273.16K= 0.01C).

SI Units: OthersSI units also exist for:

electric current

the amount of a substance

luminous intensity

***These units will be introduced as we encounter the topics throughout this course.PSSA Prep:Two streams begin at the same elevation and have equal volumes. Which statement best explains why one stream could be flowing faster than the other stream?

A.The faster stream contains more dissolved minerals.

B.The faster stream has a much steeper gradient.

C.The streams are flowing in different directions.

D.The faster stream has a temperature of 10C, and the slower stream has a temperature of 20C.

Scientific NotationIn scientific notation, all numbers are written in the form:

A x 10B C-Where A is a real number between 1 and 10

-Where B is an integer

- Where C is the unit of measurementScientific NotationA x 10B -The notation x 10B can be interpreted as multiply A by ten B timesExample: 3.5 x 104 m = 3.5 x 10 x 10 x 10 x 10 m = 35,000 m

-When B is negative, it should be interpreted as multiply A by one-tenth B timesExample:

Scientific NotationPractice: Put these numbers into scientific notation:

49,000 m

.00598 Kg

36,000,000 sSignificant Digits-Significant Digits are the digits in a measurement that are reliable.Identifying Significant Digits:1. Nonzero digits are always significant.

2. All final zeros after the decimal point are significant.

3. Zeros between two other significant digits are always significant.

4. Zeros used solely as placeholders are not significant.Significant DigitsHow many significant digits does each number have?A.) 15.45 mB.) 306.29 kgC.) 0.00436 LD.) 34.07900 JE.) 8.51 x 106 mThe Rules:

1. Nonzero digits are always significant.

All final zeros after the decimal point are significant.

3. Zeros between two other significant digits are always significant.

4. Zeros used solely as placeholders are not significant.

Significant Digits-These digits affect whether or not certain calculations make sense to perform.

Example: A man is measuring a hallway in which he plans to install carpet. He measures the hallway and records it to be 12 m long. When his wife gets home, she asks if he remembered that the carpet must go under the baseboards. He truthfully states that he didnt.Should he add the extra 0.08 meters to his measurement? Why or why not?

Significant DigitsAddition and Subtraction:Find the least precise measurement, perform the operation, and round the answer to the same place as the least precise significant figure.

Example: Add 6.789 m + 43.5 m + 18 m

6.789 m43.9 m+18. m68.689 m= 69 mSignificant DigitsMultiplication and Division:Perform the operation, then count the significant figures of the factor with the fewest sig. figs. Round your final answer so that it has the same number of sig. figs.

Example: Divide: 205 m / .347 s / 5 s

3 sig. fig.3 sig. fig.1 sig. fig.= ?

SI Prefixeshttp://en.wikipedia.org/wiki/SI_prefix

The metric prefix is used to allow measurements to become decimal-multiples that fall between .1 and 1000. SI PrefixesThe SI prefix takes the place of the order of magnitude multiple when a measurement is written in scientific notation:8,000,000 m = 8.0 x106 m = 8.0 MmOrders of MagnitudeA way of comparing relative changes in measurements.When something is about 10x bigger than another, we say that it is one order of magnitude larger than the other.A scientist leaves 30 bacteria in a dish over night. When he returns 12 hours later, he sees that there are now 400. He accurately states that in 12 hours, the bacteria has increased its population by an order of magnitude.

Orders of MagnitudeSimpsons Power of Ten movie from Introduction Media Files

Order of magnitudeOrders of Magnitude can be used to make vague estimates for numbers that would be very difficult to find. . . These estimates are often called Fermi Estimations

When checking ones solution to a problem, or wondering whether or not a measurement was taken correctly, it is wise to check if the answer is on the correct order of magnitudeOrders of Magnitude

~ 1 byte (1 note of a song)Orders of Magnitude

~ 800 Hectobytes (A Nintendo song)Orders of Magnitude

~ 1400 kilobytes(one low quality mp3)Orders of Magnitude

~100 Megabytes(One Medium Quality .mp3 Album or 1 High quality .wav file)Orders of Magnitude

~1 gigabyte (10 .mp3 albums or 1 high quality .wav album)Orders of Magnitude

~1 terabyte (100,000 high quality .mp3 songs, or 1 music store of high quality .wav files)Resourceshttp://en.wikipedia.org/wiki/siunitsTime Service Department, United States Naval Observatory