Name:

Date and section time:

TA:

Introduction to Units and Problem Solving in Oceanography

The following is an introduction to the quantitative techniques you should be familiar with in order to complete the assignments given to you in section. Please do these exercises and make sure you are comfortable with unit conversions, rate problems, scientific notation, and cross-multiplication. Appendix 1 of your textbook has useful conversions.

This will be used by your TA to evaluate the level of math knowledge in the class.

Please show all work.

Scientific Notation

Consider how scientific notation is used to express very large or very small numbers.

Express the same values using scientific notation and standard notation (i.e. 10³ = 1000)

Try this with:

47,000 =

47,243 =

649 =

0.0179 =

2.47 x 10⁵ =

4.98 x 10^-5 =

Explain how to add and subtract using scientific notation (ex: 4 x 10 ³ + 9 x 10²)

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Explain how to multiply and divide using scientific notation (ex: 4 x 10³ / 9 x 10²)

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For another example add the volume of the Pacific Ocean to the volume of the Atlantic Ocean (see Appendix 1 of your text).

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Consider why we express the distance from the Earth to the sun (about 93 million miles) in scientific notation, rather than standard notation.

Unit Conversions

Convert 47 inches to feet

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Convert 2.8 feet to inches

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Convert 2.8 feet to yards

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Convert 7.3 yards into feet

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Convert 1076 feet into miles

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Convert 2.3 miles into feet

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Show how to convert statute miles to nautical miles.

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What's a fathom in feet?

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What's a league in miles?

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Show how to convert between seconds, minutes, hours, days and years. How many seconds are in a year?

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More on Unit Conversions

What are some English and metric units of length?

English:

	

Metric:

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Of area?

English:

Metric:

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Of volume?

English:

Metric:

Of mass?

English:

Metric:

Of temperature?

English:

Metric:

Of pressure?

English:

Metric:

Convert 3 inches into centimeters.

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Fraction to decimal/percent conversions

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Fractions are often used in explaining amounts (1/2 meter), but decimal representation is much easier to use in calculations.

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How do we convert fractions into decimal form (i.e. 1/2=0.5)?

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A common application where using decimal fractions is really handy is in turning degrees of latitude and longitude into decimal notation. Normally latitude and longitude are expressed as degrees, with subdivisions of minutes and seconds. There are 60 minutes to a degree and 60 seconds in a minutes. It is sometimes necessary to express minutes and seconds as decimal fractions of a degree. How would you express 43 degrees 22 minutes as 43.xx degrees?

How are decimal and percent notation related?

Metric Prefixes and Metric Conversions

The basic units of metric measurement are:

___________ for length

___________ for volume

___________ for mass

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Prefixes are added to these units to indicate larger or smaller units, related to the basic unit by a power of 10.

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Based on the meter, (10⁰ m = 1 m), express the following prefixes in powers of 10:

Nano-

Micro-

Milli-

Centi-

Deci-

Kilo-

Mega-

Giga-

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What is a technique for converting among these different scale unit? How would you convert meters into kilometers? Kilometers into centimeters?

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Map Scaling

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Maps typically represent a much bigger area than the actual area of the map.

Consider the function of the scale of a map.

You typically find either a bar scale ( |----------|----------| ) or a numeric scale (1:24000) on a map.

Describe how to use the scale on a map to calculate the distance between two points, say the distance from Santa Cruz to Monterey, across Monterey Bay.

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For fun and extra credit, describe a map that represents something smaller than the actual are of the map.

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Rate Problems

What are some common units that express rate (speed)?

Distance?

Time?

What is the relationship between rate, time and distance?

If you know the speed of travel and the time a trip took, how do you calculate the distance traveled?

If you know distance and time, calculate rate (show formula).

If you know rate and distance, calculate time (show formula)