Carry out the following conversions. (a) 5 pm = _____ cm = _____ nm

Verified step by step guidance

1. Step 1: Understand the conversion factors. 1 picometer (pm) is equal to 1e-12 meters (m) and 1 centimeter (cm) is equal to 1e-2 meters (m). Also, 1 nanometer (nm) is equal to 1e-9 meters (m).
2. Step 2: Convert picometers to meters. Multiply the given value in picometers by the conversion factor to convert it to meters. So, 5 pm * 1e-12 = _____ m.
3. Step 3: Convert meters to centimeters. Multiply the value obtained in step 2 by the conversion factor to convert it to centimeters. So, _____ m * 1e2 = _____ cm.
4. Step 4: Convert meters to nanometers. Multiply the value obtained in step 2 by the conversion factor to convert it to nanometers. So, _____ m * 1e9 = _____ nm.
5. Step 5: Now you have the conversion of 5 pm to cm and nm.

Key Concepts

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. This involves using conversion factors, which are ratios that express how many of one unit are equivalent to another. For example, to convert picometers (pm) to centimeters (cm) or nanometers (nm), appropriate conversion factors must be applied to ensure accuracy.

Metric System

The metric system is a decimal-based system of measurement used globally, which includes units such as meters, grams, and liters. It is organized in powers of ten, making conversions straightforward. Understanding the prefixes, such as pico- (10^-12) and nano- (10^-9), is essential for converting between different metric units, such as from picometers to centimeters or nanometers.

Scientific Notation

Scientific notation is a method of expressing very large or very small numbers in a compact form, using powers of ten. For instance, 5 picometers can be expressed as 5 x 10^-12 meters. This notation is particularly useful in chemistry and physics for simplifying calculations and comparisons of quantities that vary greatly in scale.