Express the quantity 254,998 m in each unit. a. km b. Mm c. mm d. cm

Verified step by step guidance

1. Step 1: Understand the metric prefixes and their meanings. For example, 'kilo-' (k) means 10^3, 'mega-' (M) means 10^6, 'milli-' (m) means 10^-3, and 'centi-' (c) means 10^-2.
2. Step 2: Convert meters to kilometers by dividing the given value by 10^3. Use the formula: \( \text{km} = \frac{\text{meters}}{10^3} \).
3. Step 3: Convert meters to megameters by dividing the given value by 10^6. Use the formula: \( \text{Mm} = \frac{\text{meters}}{10^6} \).
4. Step 4: Convert meters to millimeters by multiplying the given value by 10^3. Use the formula: \( \text{mm} = \text{meters} \times 10^3 \).
5. Step 5: Convert meters to centimeters by multiplying the given value by 10^2. Use the formula: \( \text{cm} = \text{meters} \times 10^2 \).

Key Concepts

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to another unit. This involves using conversion factors, which are ratios that express how many of one unit are equivalent to another. For example, to convert meters to kilometers, one would use the factor that 1 km equals 1,000 m.

Metric System

The metric system is a decimal-based system of measurement used globally, which includes units such as meters (m), kilometers (km), and millimeters (mm). Each unit is based on powers of ten, making conversions straightforward. For instance, 1 km is 1,000 m, and 1 m is 1,000 mm, allowing for easy scaling between units.

Scientific Notation

Scientific notation is a way of expressing large or small numbers in a compact form, using powers of ten. For example, 254,998 m can be expressed as 2.54998 x 10^5 m. This notation is particularly useful in scientific contexts where precision and clarity are essential, especially when dealing with very large or very small quantities.