Convert rates and measurements: Metric units

Learning Objectives Identify and recall common metric prefixes and their corresponding values. Convert measurements between different metric units of length, mass, and capacity using conversion factors. Convert simple rates involving metric units (e.g., km/h to m/s). Apply unit analysis to solve multi-step conversion problems. Determine the reasonableness of a converted measurement or rate. Solve real-world problems that require converting metric units and rates. Have you ever wondered how many grams are in a kilogram of sugar, or how fast a cheetah runs in meters per second? 🐆 Understanding how to convert metric units helps us make sense of quantities in our daily lives! In this lesson, you will learn the systematic approach to converting between different metric units of...

TermDefinitionExample Metric SystemA system of measurement based on powers of ten, making conversions straightforward. It uses base units like meter (length), gram (mass), and liter (capacity).The distance from your house to school might be measured in kilometers, while the length of your pencil is measured in centimeters. Metric PrefixesPrefixes added to base units to indicate multiples or submultiples of ten. Common prefixes include kilo-, hecto-, deka-, deci-, centi-, and milli-.Kilo- means 1,000 (e.g., 1 kilometer = 1,000 meters); milli- means 0.001 (e.g., 1 millimeter = 0.001 meters). Conversion FactorA ratio of two equivalent measurements expressed in different units, used to convert from one unit to another. It is always equal to 1.The conversion factor for meters to kilometers is...

Metric Prefix Scale Each step in the metric prefix ladder represents a factor of 10. Moving left (larger units) means dividing by 10; moving right (smaller units) means multiplying by 10. To convert between metric units, identify the number of steps and direction on the prefix scale (kilo, hecto, deka, base, deci, centi, milli). For example, to convert meters to centimeters (2 steps right), multiply by $10^2$ (100). To convert grams to kilograms (3 steps left), divide by $10^3$ (1000). Unit Conversion Formula $\text{New Value} = \text{Original Value} \times \frac{\text{Desired Unit}}{\text{Original Unit}}$ This rule uses conversion factors to systematically change units. The 'Original Unit' in the denominator cancels out the 'Original Unit' in the 'O...