online metric conversion calculator

							The Metric System and Metric Conversions The Units of the Metric System The metric system is based on “basic units”: for length the base unit is the meter, volume the base unit is the liter, and for mass the base unit is the gram. For example, if we used the base unit of length in the metric system a trip from Glendora to downtown Los Angeles would be roughly 48, 280 meters. Wow! That is a large number. Is there a way to simplify this number? The metric system has many prefixes to help simplify very large or very small values. By adding a prefix before the word “meter”, we can alter the outward appearance of the value. The most common prefixes that will be used in Biology 105 are Kilo, deci, centi, and milli. Figure 1.1 shows how these prefixes are related to each other.

Kilo

large

BASE UNIT deci small centi milli micro
Figure 1.1

The Metric System and Metric Conversions If you move from the base unit up toward the prefix Kilo and place “kilo” in front of the word meter, you are describing a distance that is composed of many meters: a kilometer. If you move towards the prefix micro, you are describing a measurement that is much smaller than a meter: a micrometer. How are these prefixes related to each other?

Kilo
1000

large

BASE UNIT
10

deci
10

small

centi 10 milli
1000

micro

Figure 1.2 To understand how the prefixes are related to each other, let’s try and example. In the box marked “Base Unit” insert the word meter. First, let’s look at values smaller than
Kilo
1000

the meter. In every meter, there are 10 decimeters. In one decimeter, there are 10 centimeters. In one centimeter there are 10 millimeters. In one millimeter, there are 1000 micrometers. See how the prefix is added to

large

10

deci
10 10

the base unit “meter”? What would we do if we
centi milli

small

were measuring in grams? Now, let’s look at the values larger than
micro

1000

the meter. In order to have one Kilometer, we would need 1000 meters! 2

The Metric System and Metric Conversions Using Dimensional Analysis for Calculations One of the most powerful techniques in scientific calculations is Dimensional Analysis. These types of calculations are set up to multiply and divide according to the units within the problem. This technique allows for very complex calculations, but relies on the units or dimensions do the work for you. Often, many of these calculations could be done in your head. But what if you make a mistake? Can you retrace your steps? Should keep all of those numbers floating around in your head? No way! Here is an example of how this powerful technique works! If you had 2500 pennies, what would that equal in dollars? If you said 25 dollars – you are correct! Although you can do this calculation in your head, how could you do this calculation using dimensional analysis? Problem: 2500 pennies  dollars? 2500 pennies X 1 dollar = 100 pennies 25.00 dollars

Step 1: Set up units Units you are in X Units you want to be in = Units you want to Units you are in be in Then – the units can cancel out! Units you are in X Units you want to be in = Units you want to Units you are in be in Step 2: Put in Values ??? dollar ??? pennies

Ask yourself “which unit is larger”? The dollar is larger. So put a “1” for the dollar. 1 dollar ??? pennies Then ask “How many pennies are in a dollar”? There are 100 pennies in a dollar. So put a “100” for the pennies. 1 dollar 100 pennies 3

The Metric System and Metric Conversions

Step 3: Plug and Chug This is calculator work! 2500 pennies X 1 dollar = 100 pennies 25.00 dollars

Converting Units – Metric to English and English to Metric Many calculations you will encounter will require a conversion of English Units to Metric Units, or visa versa. Just remember the three steps in solving dimensional analysis problems. 1. Set Up the Units 2. Put in Values 3. Plug and Chug

Problem: How many centimeters are in 14 inches?

Step 1: Set up the Units In this problem, you need to change inches into centimeters. In order to accomplish this, a conversion factor is needed. Just as a word in Spanish has a word in English that means the same thing, there are conversion factors in English Units that have the same value in Metric Units. Many common conversion units are given to you on the next page. Which conversion unit can you use to solve this problem? Let’s use 1 inch = 2.54 cm as our conversion factor To set up the units in this problem – inches X cm = inches cm = inches ??? cm

inches X

???

cm

4

The Metric System and Metric Conversions Step 2: Put in Values Now we will put in the values according to the conversion factor. 14 inches X 2.54 cm 1 inch Step 3: Plug and Chug! 14 inches X 2.54 cm inch = 35.56 cm = ??? cm

Try another problem!

Problem: A gas tank holds 14 gallons of gasoline. How many liters does the tank hold? Step 1: Set up the Units In this problem, we are converting from gallons to liters. Since we are converting from English units to Metric units we need a conversion factor. 1 gallon = 3.785 liters gallons X liters = ????? liters gallons

gallons X

liters = ????? liters gallons

Step 2: Put in Values Put in the values according to the conversion factor. 14 gallons X 3.785 liters = ????? liters 1 gallon

Step 3: Plug and Chug! 14 gallons X 3.785 liters = 52.99 liters 1 gallon

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The Metric System and Metric Conversions Length: 1 cm 1 meter 1 kilometer 1 inch 1 yard 1 mile Area: 1 sq. cm 1 sq. meter 1 sq. km 1 sq. ft. 1 sq. yd. 1 sq. mile = = = = = = 0.155 sq. inch 1.2 sq. yd. 0.386 sq. miles 929 sq. cm 0.831 sq. m. 2.59 sq. km. = = = = = = 0.394 inches 39.4 inches 0.621 miles 2.54 cm (centimeters) 0.914 m (meters) 1.61 km (kilometers)

Volume (solids): 1 cu. ft. 1 cu. yd. (liquids) 1 oz. 1 qt. 1 gal Mass: 1 gram 1 kilogram 1 pound Temperature:
o o

= =

28,320 cm3 0.7646 m3

= = =

29.6 ml 0.946 liters 3.785 liters

= = =

0.0353 oz. 35.28 oz. (or 2.2 pounds) 454 grams

C F

= =

5/9(oF - 32) or (oF - 32)/1.8 (9/5 oC + 32) or (1.8 oC) + 32

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