Measurement - Metric System of Measurement (Length, Mass, Capacity)

The Metric System is a decimal-based system of measurement used globally. It relies on powers of $10$, making conversions simple by moving the decimal point. The base units you must know are meters ($m$) for length, grams ($g$) for mass, and liters ($L$) for capacity.

The Metric Staircase is a visual tool to remember prefixes. Imagine a set of stairs: Kilo- ($1000$), Hecto- ($100$), Deca- ($10$), Base Unit ($1$), Deci- ($0.1$), Centi- ($0.01$), and Milli- ($0.001$). When moving 'down' the stairs to a smaller unit, you multiply by $10$ for each step. When moving 'up' to a larger unit, you divide by $10$ for each step.

Measuring Length involves units like millimeters ($mm$), centimeters ($cm$), meters ($m$), and kilometers ($km$). To visualize these: a millimeter is roughly the thickness of a credit card, a centimeter is about the width of your fingernail, a meter is the distance from the floor to a doorknob, and a kilometer is about a $10$-minute brisk walk.

Measuring Mass refers to how much matter is in an object, using milligrams ($mg$), grams ($g$), and kilograms ($kg$). Visually, a small paperclip weighs about $1 \text{ g}$, while a large $1 \text{ L}$ bottle of water has a mass of approximately $1 \text{ kg}$. Note that in the metric system, mass and weight are often used interchangeably in daily life, though they differ in physics.

Measuring Capacity (Volume) describes how much liquid a container can hold, primarily using milliliters ($mL$) and liters ($L$). Imagine a standard teaspoon holds $5 \text{ mL}$ of liquid, whereas a large carton of milk typically holds $1 \text{ L}$. A key visual link is that $1 \text{ cm}^3$ of volume is exactly equal to $1 \text{ mL}$ of capacity.

Conversion Rule of Thumb: To convert from a large unit to a small unit (e.g., $kg$ to $g$), you 'multiply' because you will have more of the smaller units. To convert from a small unit to a large unit (e.g., $mL$ to $L$), you 'divide' because the larger units cover more space.