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Chapter 6: Problem 48

Convert to standard notation. $$ \text { 5.8 million } $$

Short Answer

Expert verified
5,800,000

Step by step solution

01

Understand the Problem

The task is to convert '5.8 million' into standard notation. Standard notation means writing the number without using words like 'million'.
02

Identify the Value of 'Million'

Recall that 1 million is equivalent to 1,000,000 or can be written as 10^6 in scientific notation.
03

Multiply by the Value of 'Million'

Since 5.8 million means 5.8 times 1,000,000, we perform the multiplication: \[ 5.8 \times 1,000,000 = 5,800,000 \]
04

Write the Final Answer in Standard Notation

The standard notation of 5.8 million is 5,800,000.

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Key Concepts

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

million conversion
Understanding how to convert millions into standard notation is essential. When we hear '5.8 million,' it can be tricky to grasp the actual number. To break it down simply, a 'million' is the same as 1,000,000. Hence, converting millions to standard notation involves identifying the number given (in this case, 5.8) and multiplying it by 1,000,000.
This turns the phrase '5.8 million' into a numerical expression. For example,
  • 5.8 million becomes 5.8 脳 1,000,000.

By understanding what a million represents and performing the multiplication, we get the standard form: 5,800,000. Therefore, 'million conversion' means replacing the word 'million' with its numerical equivalent.
multiplication with large numbers
Handling large numbers in multiplication requires a clear and methodical approach. When you multiply a smaller number by a large one like 1,000,000, it's helpful to break it down. For instance, consider the steps in our example:
We start with 5.8 and need to multiply by 1,000,000. This can seem daunting at first, but by breaking it down, it gets simpler.
Remember, multiplication is repetitive addition. In this case,
  • We use the rule:
    5.8 脳 1,000,000 means adding 1,000,000 to itself 5.8 times.
  • Instead of adding 1,000,000 5.8 times, which is impractical, multiplication does it for us.
  • The result is 5,800,000, confirming our conversion.

Always ensure your decimal placement is correct when dealing with large number multiplications to avoid errors.
scientific notation
Scientific notation is a powerful tool for expressing large numbers, making them easier to read and work with. Instead of writing out many zeros, we use powers of 10. To understand this, look at our 1,000,000 example:
1,000,000 in scientific notation is written as
  • \(1 \times 10^6\).

Applying this to our number:
5.8 million becomes
  • \(5.8 \times 10^6\).

Each time you move a place value to the left, you increase the exponent of 10 by one.
This notation helps to efficiently handle very large or very small numbers and is particularly useful in fields like science and engineering. Transitioning between scientific notation and standard notation can aid in understanding the scale of numbers better.

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