Math 801A: Mathematical Operations – Metric Conversions Mathematics Essentials March 14th, 2017

Lesson Introduction Today I will... convert between measurements mentally when appropriate convert between measurements within, or between, systems of measurement using the concept of rate select and use appropriate measuring devices involving metric measurement

Measuring Activity Pg. 53 – Activity and #1-5. Using a metric tape measure, complete the table by measuring three objects or locations of choice. The measurements provided for each object or location are equalities (of equal value).

Metric System Based on factors of 10 A quantity can be expressed in several ways simply by changing the unit of measure and modifying the number that correlates with the unit (e.g. 1 m = 1000 mm)

Measurement and Metric Units Millimeters (mm) Centimeters (cm)

Measurement and Metric Units Decimeters (dm) Kilometers (km) Meters (m)

Metric Prefixes Multiple of Base Unit Prefix Name Prefix Symbol Actual Magnitude 1012 tera T 1 000 000 000 000 109 giga G 1 000 000 000 106 mega M 1 000 000 103 kilo k 1 000 102 hecto h 100 101 deca da 10 Base Unit 1 10-1 deci d 0.1 10-2 centi c 0.01 10-3 milli m 0.001 10-6 micro µ 0.000 001

Base Units Metric system contains a variety of base units: Meter, m (length) Liter, L (volume) Gram, g (mass) Ampere, A (current) Volt, V (voltage) Ohm, Ω (resistance) Base units don’t contain a metric prefix

Unit Conversion (Shifting the Decimal) Step 1: figure out what unit is larger, the one you are given or the one to which you are converting Step 2: if the unit you are given is smaller than the unit you are shifting to (e.g. cm to m), the new measurement should have a smaller numeric value (example 1). If the unit you are given is larger than the unit you are shifting to (e.g. kL to L), the new unit should have a larger numeric value (example 2).

Unit Conversion (Conversion Factors) Requires equalities to be written (similar to common 16th decimal conversion) Step 1: write the equality that relates the two units (conversion factor) Step 2: Multiply the given measurement by the conversion factor such that the units cancel.

Homework! Unit Conversion Assignment due Friday: Pg 56, #1 all