Write the equality and two conversion factors for each of the following pairs of units:
b. nanograms and grams

Verified step by step guidance

1. Step 1: Understand the relationship between nanograms (ng) and grams (g). The prefix 'nano-' means 10^-9, so 1 nanogram (ng) is equal to 10^-9 grams (g).
2. Step 2: Write the equality that relates nanograms to grams: 1 ng = 10^-9 g.
3. Step 3: From the equality, derive the first conversion factor. To convert from nanograms to grams, use the factor: \( \frac{10^{-9} \text{ g}}{1 \text{ ng}} \).
4. Step 4: Derive the second conversion factor. To convert from grams to nanograms, use the factor: \( \frac{1 \text{ ng}}{10^{-9} \text{ g}} \).
5. Step 5: Summarize the equality and the two conversion factors: Equality: 1 ng = 10^-9 g. Conversion factors: \( \frac{10^{-9} \text{ g}}{1 \text{ ng}} \) and \( \frac{1 \text{ ng}}{10^{-9} \text{ g}} \).

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. Understanding unit conversion is essential for accurately comparing and calculating measurements in different units.

Metric System

The metric system is a decimal-based system of measurement used worldwide, which includes units such as grams, kilograms, and nanograms. In this system, each unit is based on powers of ten, making conversions straightforward. For example, one gram is equal to one billion nanograms, illustrating the hierarchical nature of metric units.

Conversion Factors

Conversion factors are numerical values used to convert one unit of measurement to another. They are derived from the equivalence between different units, such as 1 gram = 1,000,000,000 nanograms. By multiplying a quantity by the appropriate conversion factor, one can easily switch between units while maintaining the same quantity.