Determining Conversion Factors for Metric Units

Transcription

1 Determining Conversion Factors for Metric Units Reading: Section 2.2: Units PRELAB ASSIGNMENT: Complete on a separate sheet. Your answer should be typewritten. Define: Base unit English system Metric system International system (SI) MATERIALS Equipment: Meter stick (with increments of mm, cm, dm, and m) HAZARDS The materials used in this laboratory exercise are not known to be dangerous; however, caution should always be exercised in the laboratory. PROCEDURE 1. Using your meter stick, determine each of the following. Record your answers in your data section. a. How many decimeters are there in one meter? b. How many centimeters are there in one meter? c. How many millimeters are there in one meter? d. How many centimeters are there in one decimeter? e. How many millimeters are there in one decimeter? f. How many millimeters are there in one centimeter? 2. One kilometer is one thousand (10 3 ) times bigger than a meter. Using your meter stick, determine each of the following. Record your answers in your data section. a. How many meters are there in one kilometer? b. How many decimeters are there in one kilometer? c. How many centimeters are there in one kilometer? d. How many millimeters are there in one kilometer? 3. One micrometer is one thousand (10 3 ) times smaller than a millimeter. Using your meter stick, determine each of the following. Record your answers in your data section. a. How many micrometers are there in one millimeter? b. How many micrometers are there in one centimeter? c. How many micrometers are there in one decimeter? d. How many micrometers are there in one meter? 1

2 DISCUSSION If one quantity is ten (10 1 ) times bigger than another quantity, then they are different by one order of magnitude. If one quantity is one hundred (10 2 ) times bigger than another quantity, then they are different by two orders of magnitude. If one quantity is one thousand (10 3 ) times bigger than another quantity, then they are different by three orders of magnitude. If one quantity is one million (10 6 ) times bigger than another quantity, then they are different by six orders of magnitude. If one quantity is one billion (10 9 ) times bigger than another quantity, then they are different by nine orders of magnitude. Prefix Order of Magnitude What does this mean? Difference from Base Unit Tera (T) A Tera is one trillion times larger Giga (G) 10 9 A Giga is one billion times larger Mega (M) 10 6 A Mega is one million times larger Kilo (k) 10 3 A kilo is one thousand times larger Deci (d) 10 1 A deci is ten times smaller (one tenth) Centi (c) 10 2 A centi is one hundred times smaller (one one hundredth) Milli (m) 10 3 A milli is one thousand times smaller (one one thousandth) Micro (µ) 10 6 A micro is one million times smaller (one one millionth) Nano (n) 10 9 A nano is one billion times smaller (one one billionth) Pico (p) A pico is one trillion times smaller (one one trillionth) How can we apply this table to writing conversion factors? Example 1: The difference in order of magnitude between kilo and mega is Therefore, a megameter is 10 3 (one thousand) times bigger than a kilometer. This can be written as 10 3 km = 1 Mm or 10 3 km 1 Mm 2

3 Example 2: The difference in order of magnitude between kilo and giga is Therefore, a gigabyte is 10 6 (one million) times bigger than a kilobyte. This can be written as 10 6 kbyte = 1 Gbyte or 10 6 kbyte 1 Gbyte Example 3: The difference in order of magnitude between centi and kilo is Therefore, a kilogram is 10 5 (ten thousand) times bigger than a centigram. This can be written as 10 5 cg = 1 kg or 10 5 cg 1 kg DATA Example: The number of km in one Mm 1000, or 10 3 The number of decimeters in one meter The number of centimeters in one meter The number of millimeters in one meter The number of centimeters in one decimeter The number of millimeters in one decimeter The number of millimeters in one centimeter The number of meters in one kilometer The number of decimeters in one kilometer The number of centimeters in one kilometer The number of millimeters in one kilometer The number of micrometers in one millimeter The number of micrometers in one centimeter The number of micrometers in one decimeter The number of micrometers in one meter OBSERVATIONS Record your observations below. 3

4 ANALYSIS 1. Write conversion factors to represent each of the data you gathered. Example: kilometer and megameter 10 3 km = 1 Mm or 10 3 km 1 Mm decimeter and meter centimeter and meter millimeter and meter centimeter and decimeter millimeter and decimeter millimeter and centimeter meter and kilometer decimeter and kilometer centimeter and kilometer millimeter and kilometer micrometer and millimeter micrometer and centimeter micrometer and decimeter micrometer and meter 4

5 2. Re write the same conversion factors, this time referring only to the table given in the discussion. decimeter and meter centimeter and meter millimeter and meter centimeter and decimeter millimeter and decimeter millimeter and centimeter meter and kilometer decimeter and kilometer centimeter and kilometer millimeter and kilometer micrometer and millimeter micrometer and centimeter micrometer and decimeter micrometer and meter 5

6 3. Compare your answers to #1 & #2 to make sure that you know how to use the table and/or ruler! 4. Using the table given in the discussion, write conversion factors for each of the following: a. Nanograms and micrograms b. Milligrams and kilograms c. Gigabyte and terabyte d. Megabyte and gigabyte e. Kilometers and micrometers 6