Explain exponential notation and write one billion in exponential notation.

Here are the answers to your questions:

7) Your cousin wrote $10^5$ in her maths book. This means that the number 10 is multiplied by itself 5 times.

$$10^5 = 10 \times 10 \times 10 \times 10 \times 10 = 100,000$$

It represents the number one hundred thousand.

8) Exponential notation is used in many practical situations:

• Scientific notation: To express very large or very small numbers in science, such as the distance to a star or the size of an atom (e.g., $3 \times 10^8$ m/s for the speed of light).
• Computer science: To describe data storage capacity (e.g., 1 kilobyte is $2^{10}$ bytes, 1 gigabyte is $10^9$ bytes).
• Population growth: To model how populations of organisms grow over time.

Problem solving: Write one billion in exponential notation.
One billion is 1,000,000,000.
In exponential notation, this is:

$$\boxed{10^9}$$