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 and grams.
2. Step 2: Recall that 1 gram is equal to 1,000,000,000 nanograms. This is because 'nano' denotes a factor of 10^{-9}.
3. Step 3: Write the equality: 1 gram = 1,000,000,000 nanograms.
4. Step 4: Create the first conversion factor by expressing the equality as a fraction: \( \frac{1 \text{ gram}}{1,000,000,000 \text{ nanograms}} \).
5. Step 5: Create the second conversion factor by inverting the first: \( \frac{1,000,000,000 \text{ nanograms}}{1 \text{ gram}} \).

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 how to manipulate these factors is essential for accurately converting measurements in chemistry.

Metric System

The metric system is a decimal-based system of measurement used globally in science and everyday life. It includes units such as grams, kilograms, and nanograms, where each unit is a power of ten. Familiarity with the metric prefixes (like 'nano-' for 10^-9) is crucial for understanding the scale of measurements and performing conversions.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert between units by multiplying by conversion factors. It ensures that units cancel appropriately, leading to the desired unit in the final answer. This method is particularly useful in chemistry for ensuring that calculations involving different units are accurate and consistent.