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Chapter 5: Problem 90

Convert to decimal notation. $$ 8.001 \times 10^{7} $$

Short Answer

Expert verified
80010000

Step by step solution

01

Understand the Scientific Notation

Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. In this case, we have the number written as \(8.001 \times 10^{7}\) which means \(8.001\) is multiplied by \(10\) raised to the power of \(7\).
02

Identify the Exponent

Here, the exponent is \(7\). This means that we need to move the decimal point in \(8.001\) seven places to the right.
03

Move the Decimal Point

Starting with \(8.001\), move the decimal point seven places to the right: \(8.001 \rightarrow 80.01 \rightarrow 800.1 \rightarrow 8001 \rightarrow 80010 \rightarrow 800100 \rightarrow 8001000 \rightarrow 80010000\)
04

Rewrite in Decimal Notation

After moving the decimal point seven places to the right, \(8.001 \times 10^{7}\) can be rewritten as \(80010000\).

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Key Concepts

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

What is Scientific Notation?
Scientific notation is a method used to write very large or very small numbers more concisely. It's particularly useful in fields like science and engineering. Imagine trying to write out a number like 0.0000000000056 or 4700000000 without making mistakes! Here is the basic format for scientific notation:

  • A number between 1 and 10 (but not including 10).
  • Multiplied by a power of 10.

For example, the number 8,001,000 is written in scientific notation as\(8.001 \times 10^{7}\). This means the decimal point in 8.001 is moved 7 places to the right. This allows you to easily manage and manipulate really big or tiny numbers.
Understanding Decimal Notation
Decimal notation is the standard way of writing numbers. It's what you typically use in everyday life. Each place to the left or right of the decimal point represents a different power of 10:

  • 100 for ones
  • 101 for tens
  • 10-1 for tenths
  • 10-2 for hundredths

To convert from scientific notation to decimal notation, you move the decimal point to the right or left based on the exponent of 10. For example, converting\(8.001 \times 10^{7}\) involves shifting the decimal point 7 places to the right, resulting in 80010000.
Decoding the Exponent
An exponent tells us how many times to multiply a number by 10. In scientific notation, it appears as the small number (called the exponent) following the base of 10. For example, in\(8.001 \times 10^{7}\), the number 7 is the exponent. This indicates that the decimal point in 8.001 should be moved 7 places to the right.

Notice how the base number (8.001) changes as you move the decimal point:

  • Move 1 place: 80.01
  • Move 2 places: 800.1
  • Move 3 places: 8001
  • Move 4 places: 80010
  • Move 5 places: 800100
  • Move 6 places: 8001000
  • Move 7 places: 80010000

This process converts our scientific notation\(8.001 \times 10^{7}\) to its decimal form, 80010000.

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