Problem 113 - Algebra A Combined Function

Question

For Exercises 113-118, write each number in standard form. Then write the number in scientific notation. The Facebook Web site has more than 90 million active users.

Step-by-Step Solution

Answer

Standard form: 90,000,000; Scientific notation: \(9.0 \times 10^7\).

Step 1: Understand the Context

We are given a number, "more than 90 million," which indicates the number of Facebook active users. Our task is to express this number in standard form and then in scientific notation.

Step 2: Express in Standard Form

In standard form, we can express "more than 90 million" as the number 90,000,000. This is because 1 million is equal to 1,000,000, so 90 million equals 90 multiplied by 1,000,000.

Step 3: Convert to Scientific Notation

Scientific notation expresses numbers as the product of a number (between 1 and 10) and a power of 10. For 90,000,000, we can rewrite it as 9.0 multiplied by 10 to the power of 7, or in scientific notation: \(9.0 \times 10^7\).

Key Concepts

Standard Form

Standard form is a way of writing numbers that is widely used in everyday mathematics. It means writing the number without using any commas. If a number has many zeros, putting it into standard form helps make it tidier and easier to read. For example, the number "90 million" when written in standard form is 90,000,000. This is because one million is a "1" followed by six zeros, and thus 90 million is 90 multiplied by a million.
The standard form is especially useful for expressing numbers clearly in pieces of financial data, population figures, or anywhere else where large numbers are common. It helps eliminate confusion and errors that might occur when dealing with many zeros. Learning to write numbers in standard form is a foundational skill for understanding both everyday math and more advanced topics.

Large Numbers

Large numbers can be intimidating, but they are just extended versions of smaller numbers. When we talk about large numbers, we usually mean numbers that go beyond thousands into millions, billions, and even beyond. These numbers often appear in contexts such as population counts, astronomical data, and scientific measurements.
To understand large numbers, it helps to break them down. Remember, a million is a thousand thousands. Therefore, knowing this can help us see that 90 million is simply 90 multiplied by a million, which is 90,000,000.
In dealing with large numbers, it's crucial to grasp their magnitude without getting lost in the zeros. This is exactly why tools like scientific notation are handy – they let us handle these massive figures with ease, leaving no room for error.

Mathematical Conversion

Mathematical conversion, especially when talking about numbers, involves changing numbers from one form to another without altering their value. In the context of our problem, we first converted the number "more than 90 million" into standard form, as 90,000,000. Afterward, we converted it into scientific notation.
Scientific notation is a way of writing very large or very small numbers using powers of ten. It simplifies the representation and is particularly useful in scientific and mathematical contexts where it is common to deal with such numbers. In our example, 90,000,000 becomes 9.0 multiplied by 10 to the power of 7, written as \(9.0 \times 10^7\).
Converting numbers helps in computations and understanding large quantities without confusion. Remember, the base of scientific notation is always between 1 and 10, making it a manageable figure, multiplied by a power of ten that designates the scale of the original number. This conversion process is fundamental in science and engineering.