Using the Metric System

Transcription

1 C H E M I S TRY I METRIC REVIEW Using the Metric System On Sept., 1999, a $15 million Mars orbiter went missing. The loss occurred because the engineering team that designed part of the orbiter used Imperial units of measurement, while the NASA team that designed other parts of the orbiter used metric units. The difference in measurement units prevented navigation information from being transferred between the teams controlling the orbiter. The loss of the Mars orbiter illustrates the importance of using consistent, easily understandable units to describe scientific measurements. Scientists all over the world use the metric system to reduce the chances of misunderstanding. The term metric is derived from the Greek word metron, which means to measure. Metric system units can be converted from one to another simply by moving the decimal to the right or to the left. The metric system is based on several basic units such as the gram, the second, and the meter. Prefixes are used to indicate the number of basic units in a measurement. Prefixes for Multiples of Metric Units Factor Prefix Symbol 1,000,000,000 = 10 9 giga- G 1,000,000 = 10 6 mega- M 1,000 = 10 kilo- k 100 = 10 hecto- h 10 = 10 1 deka- da 0.1 = 10-1 deci- d 0.01 = 10 - centi- c = 10 - milli- m = 10-6 micro- μ = 10-9 nano- n = 10-1 pico- p The bolded prefixes are ones you will most commonly encounter in this course. Metric Units Units of Mass Measurements of mass are based on the gram (g) grams (g) = 1 kilogram (kg) 1000 milligrams (mg) = 1 gram (g) Units of Length Measurements of length are based on the meter (m). 100 centimeters (cm) = 1 meter (m) 1000 meters (m) = 1 kilometer (km) 1000 millimeters (mm) = 1 meter (m)

2 Units of Volume Measurements of volume are based on the liter (L). 1 cubic centimeter (cc or cm ) = 1 milliliter (ml) 1000 milliliters (ml) = 1 liter (L) You can use the equalities you just saw as conversion factors to convert one unit into another. You do this by setting up the equalities as ratios that all represent a value of 1. If two things are equal to each other, they represent the same thing; thus, their ratio will equal 1. For example, look at the ratios below: 1000 ml = 1 1 L because 1000 ml = 1 L 1 dm = 1 1 L because 1 dm = 1000 ml = 1 L 1 ml = 1 1 cm because 1 ml = 1 cm 1000 mg = 1 1 g because 1000 mg = 1 g Let's look at some examples of converting between metric units. Suppose you have 00 ml of hydrochloric acid. How many liters of acid do you have? To solve this problem, use the equality between milliliters and liters, as shown below: 00 ml 1 L 1000 ml = 0.00 L Because the unit ml appears both above and below the denominator, you can cancel it out. The only unit that remains is liters. A chemist has kg of copper sulfate powder. How many micrograms (µg) of powder does she have? Again, use equalities to convert between units. Here we use two equalities: one to convert kilograms to grams and another to convert grams to micrograms. This helps prevent errors in calculation. kg 1000 g 1,000,000 μg 1 g =,000,000,000 μg This number has many zeros in it, which can make it difficult to read. To make numbers like this easier to read, you can rewrite them in scientific notation.

3 Remember that a number in scientific notation consists of a number multiplied by a power of ten. For example, the answer above (which has 9 zeros after the ) would be written like this: 10 9 μg Scientific notation allows us to write very large or very small numbers without writing every zero. Now that you know how to use equalities as conversion factors, try the following conversions. Check the answers to make sure you are setting them up correctly. For practice, write your answers in scientific notation. a. 50 m =? km b. 8. kg =? g c. 50 m =? cm d. 78 mg =? kg e..5 cm =? mm f kg =? mg g mm =? km h..800 L =? cm

4 Key a. 50 m =? km 1 km 50 m = 0.05 km = 510 km 1000 m b. 8. kg =? g 8. kg 1000 g = 800 g = 8.10 g c. 50 m =? cm 100 cm 50 m = 5000 cm = 510 cm 1 m d. 78 mg =? kg 78 mg 1 g 1000 mg 1000 g = kg = kg Or, using an alternative conversion factor: 78 mg 1,000,000 mg = kg = kg e..5 cm =? mm.5 cm 1 m 1000 mm 100 cm 1 m 1 = 5 mm =.510 mm Or, using an alternative conversion factor:.5 cm 10 mm 1 cm 1 = 5 mm =.510 mm

5 f kg =? mg 7.10 kg 1000 g 1000 mg 1 g Alternatively: = 70 mg = 7.10 mg 1,000,000 mg 7.10 kg = 70 mg = 7.10 mg g mm =? km 1 m 1 km mm = km = km 1000 mm 1000 m Alternatively: 1 km mm = km = km 1,000,000 mm h..800 L =? cm.800 L 1000 cm 1 L = 800 cm =.810 cm Copyright 010 A+, A+LS, A+ VLabs and A+nyWhere Learning System are trademarks or registered trademarks of American Education Corporation. All rights reserved. 5