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# Read Sections 1.9 and Appendix A.2 before viewing this slide show. - PowerPoint PPT Presentation

Read Sections 1.9 and Appendix A.2 before viewing this slide show. Unit 4 Measurement – Basic Units. The International System of Units (SI) (1.9) Current definitions of the seven base SI units Review of exponential notation (Appendix A.2) Metric prefixes and their interconversion (1.9).

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Read Sections 1.9 and Appendix A.2 before viewing this slide show.

Measurement – Basic Units

• The International System of Units (SI) (1.9)

• Current definitions of the seven base SI units

• Review of exponential notation (Appendix A.2)

• Metric prefixes and their interconversion (1.9)

• Adopted in 1960 – defines standard units to be used in measurement of seven basic properties as given below.

• Six of the units have very well defined, though somewhat abstract, descriptions. For example,

• second: The second is 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 cesium-133 atom.

• meter: The meter is the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second.

• Definitions of the other four that have precise definitions may be found at http://physics.nist.gov/cuu/Units/current.html

• The kilogram is the only one not precisely defined – see next slide.

• The kilogram is called a prototype standard – there is one chunk of matter that is “the” kilogram as pictured.

• The official kilogram resides inFrance. Several copies are inexistence throughout theworld.

• Concern was raised in 2007 that the kilogram is losing mass – about50 millionths of a gram in 100 years.This is roughly the mass of afingerprint.

• Looking at the SI base units gives a strong sense that it is a metric-based system

• The metric system depends heavily on the ability to maneuver the decimal point in a number

• Some of the numbers we will see during the semester are incredibly large or incredibly small and we must have a system to write and work with these numbers without difficulty

• Thus there is a need to be conversant in exponential notation (sometimes called scientific notation)

• The concept of exponential notation is based on our base 10 number system:

• In the left column, where the numbers are greater than 1, the power on 10 is the number of decimal places to the right of the digit “1”

• In the right column, where the numbers are less than 1, the exponent on 10 is negative and is the number of decimal places from the decimal place to that just after the digit “1"

Examples of Converting Between Standard Notation and Exponential Notation

• Consider the following conversions:

63410 m = 6.3410 x 104 m

145.6 s = 1.456 x 102s

0.00389 kg = 3.80 x 10-3 kg

9.87 x 104 L = 98700 L

5.12 x 10-5 cm = 0.0000512 cm

Metric Prefixes (1.9) Exponential Notation

• Part of the beauty of the metric system is that conversion of units is simply a matter of moving the decimal point. Metric prefixes are used to indicate the size of the unit. Some of the more common metric prefixes are given in the table below.

Metric Conversions Exponential Notation

• Notice in the table:

• The difference in exponents between two prefixes gives the number of decimal places to be moved in a conversion

• If the conversion is from a larger unit to a smaller unit (down the table), the decimal point is movedto the right

• If the conversion is from a smaller unit to a larger unit (up the table), the decimal point is moved to the left

• See examples on the next page

Move Right

Move Left

Examples of Metric Conversion Exponential Notation

42600 m = 42.6 km

(m to km is three decimal places, since going up the table move three decimal places to the left)

0.459 km = 45900 cm

(km to cm is five decimal places, since going down the table move five decimal places to the right)

350 mL = 0.350 L

(mL to L is three decimal places, since going up the table move three decimal places to the left)

4.52 x 1034ds = 4.52 x 1035cs

(ds to cs is one decimal place, since going down the table move to the right making the exponent bigger by one)

Move Right

Move Left

The End Exponential Notation