Knowing Our Numbers - Large Numbers in Practice

Understanding Large Units: In practice, we use larger units to measure distance, mass, and capacity. For length, we use kilometers ($km$), meters ($m$), centimeters ($cm$), and millimeters ($mm$). Visualize a long highway measured in $km$, while the thickness of a cardboard is measured in $mm$.

Units of Mass and Capacity: Mass is measured in kilograms ($kg$), grams ($g$), and milligrams ($mg$). Capacity is measured in liters ($L$) and milliliters ($mL$). Imagine a large sack of rice weighing $25 \text{ kg}$ versus a small medicine tablet weighing $250 \text{ mg}$.

Unit Conversion Rules: To convert from a higher (larger) unit to a lower (smaller) unit, we multiply by the conversion factor. To convert from a lower unit to a higher unit, we divide. Think of a 'Conversion Staircase' where jumping down steps requires multiplication and climbing up requires division.

Estimation and Rounding: Estimation gives a rough idea of a quantity rather than an exact value. To round to the nearest ten, look at the ones digit: if it is $5$ or more, round up; otherwise, round down. On a number line, the number $48$ is closer to $50$ than $40$, so it rounds to $50$.

Estimating Outcomes: We estimate the results of addition, subtraction, multiplication, and division by rounding numbers to their greatest place value. For example, estimating $5,290 + 17,986$ involves rounding both to the nearest thousand to get $5,000 + 18,000 = 23,000$.

Using Brackets: Brackets are used to simplify expressions and ensure the correct order of operations. For example, if you buy $5$ pens at $10$ rupees each and $5$ pencils at $2$ rupees each, the total cost is $5 \times (10 + 2)$, which simplifies the calculation by grouping the quantities.

Roman Numerals: This system uses seven basic symbols: $I=1, V=5, X=10, L=50, C=100, D=500, M=1000$. Rules include: symbols $I, X, C, M$ can be repeated up to three times, and if a smaller value symbol is placed before a larger one, it is subtracted (e.g., $IV = 5 - 1 = 4$).