M ETRIC C ONVERSIONS

T HE M ETRIC S YSTEM Scientists use the metric system of measurement. The metric system is different from the system of measurement used in the U.S. The metric system can be easier to use because it is based on powers of ten.

B ASE U NITS Each quantity is measured by a base unit. Base units are the standard units used to measure each quantity. The most common base units are: Length – meter Mass – gram Volume – liter

M ETRIC P REFIXES Prefixes are added to the base units to show very large or very small quantities. PrefixMeaning Numerical Value MilliOne thousandth.001 CentiOne hundredth.01 DeciOne Tenth.1 Base Unit DekaTen10.0 HectoOne Hundred100.0 KiloOne Thousand1,000.0

M ETRIC P REFIXES Prefixes help condense numbers to make them more manageable. Example: The distance of a charity race is measured as 5000 meters. This same quantity can be expressed as 5 kilo meters.

M ETRIC C ONVERSIONS Measurements can be converted or changed from one unit to another. Only measurements that use the same base unit can be converted (centimeters to millimeters, or kilograms to grams). Cannot convert measurements with different base units because they measure different things grams measure mass, meters measure length, etc.

C ONVERSION F ACTORS When converting from one unit to another, multiply the number given in the problem by the conversion factor. Conversion factors show how many of the smaller units are in the larger unit. Example: There are 100cm in 1m The smaller unit gets the bigger number and the larger unit gets a 1. The number in front of the small unit depends on which prefix is being used. Centi- means one hundredth, so a centimeter is 1/100 of a meter Example: 100cm or 1m 1m 100cm

S ETTING U P C ONVERSIONS Rules for setting up conversion factors: 1. The unit given in the problem goes on the bottom of the fraction. 2. The unit you are trying to find goes on the top. 3. The larger unit will always get a The smaller unit gets the larger number, depending on the prefix being used.

C ONVERSIONS – L ARGE TO S MALL U NITS Example Problem: How do you convert 1.85m into centimeters? Meters are given in the problem (goes on bottom). We are trying to find centimeters (goes on top). Meters are bigger than centimeters, so meters gets a 1. There are 100cm in a meter, so the conversion factor is 100cm 1m 1.85m x 100cm = 185cm 1m

C ONVERSIONS - S MALL TO L ARGE U NITS Example Problem: How do you convert 185cm into meters? Centimeters are given in the problem (goes on bottom). We are trying to find meters (goes on top). Meters are larger than centimeters, so meters gets a 1. There are 100cm in a meter, so the conversion factor is: 1m 100cm 185cm x 1m = 1.85m 100cm

P RACTICE P ROBLEMS – L ARGE TO S MALL U NITS 1. Convert 1.6 kilograms (kg) to grams (g) 2. Convert 3.65 liters (L) to milliliters (mL) 3. Convert 2.75 meters (m) to centimeters (cm)

P RACTICE P ROBLEMS – L ARGE TO S MALL U NITS (A NSWERS ) kg x 1000g = 1600g 1kg L x 1000mL = 3650mL 1L m x 100cm x = 275cm 1m

P RACTICE P ROBLEMS – S MALL TO L ARGE U NITS 1. Convert 550 millimeters (mm) to meters (m) 2. Convert 45 decigrams (dg) to grams (g) 3. Convert 90 liters (l) to dekaliters (dal)

P RACTICE P ROBLEMS – S MALL TO L ARGE U NITS (A NSWERS ) mL x 1L = 0.550L 1000mL 2. 45dg x 1g = 4.5g 10dg 3. 90L x 1dal = 9dal 10L