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Chapter 6: Problem 50

Convert to standard notation. $$ 6.09 \text { billion } $$

Short Answer

Expert verified
6,090,000,000

Step by step solution

01

Understand the Problem

To convert 6.09 billion to standard notation, recognize that 'billion' refers to the value \(10^9\).
02

Multiply by the Value of Billion

Multiply 6.09 by the value of a billion, which is \(10^9\). So, we have: \(6.09 \times 10^9\).
03

Perform the Multiplication

Now, calculate the product: \(6.09 \times 10^9 = 6,090,000,000\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

large numbers
Large numbers can be intimidating, but they are just numbers with a lot of digits. Common large numbers include millions, billions, and trillions. For instance, a million has six zeros (1,000,000), a billion has nine zeros (1,000,000,000), and a trillion has twelve zeros (1,000,000,000,000).
Understanding these large numbers helps in daily life because they are often used in contexts like population counts, national budgets, and distances in astronomy.
To make these numbers easier to handle, we often convert them into more manageable forms, like in scientific notation.
scientific notation
Scientific notation is a way to write large (or small) numbers compactly. It's particularly useful in science and engineering.
In scientific notation, a number is written as the product of two factors: a coefficient that is at least 1 but less than 10, and a power of ten. For example, a billion (1,000,000,000) is written as \(1 \times 10^9\).
Here鈥檚 how to convert to scientific notation:
  • Place the decimal point after the first non-zero digit.
  • Count how many places you moved the decimal. This becomes your power of ten.
  • For example, 6,090,000,000 becomes 6.09 because the decimal point moves 9 places to the left, resulting in \(6.09 \times 10^9\).
mathematical conversion
Mathematical conversion helps switch numbers between different forms, like from standard notation to scientific notation, and vice versa. This can simplify calculations and comparisons.
To convert a number like 6.09 billion into standard notation, follow these steps:
  • Recognize the term 'billion' means \(10^9\).
  • Multiply the number (6.09) by \(10^9\).
  • Performing this calculation gives you 6,090,000,000.
    Hence, 6.09 billion in standard notation is 6,090,000,000.
Converting back involves reversing the process. If you have 6,090,000,000, you would express it as 6.09 times 10 to the power of 9 in scientific notation.

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