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Chapter 10: Problem 398

In the following exercises, convert each number to decimal form. $$5.5 \times 10^{8}$$

Short Answer

Expert verified
550,000,000

Step by step solution

01

Identify the Scientific Notation Components

Recognize that the given number is in scientific notation. The number is expressed as: \[5.5 \times 10^{8}\]The coefficient is 5.5, and the exponent is 8.
02

Understand What the Exponent Means

The exponent indicates how many places to move the decimal point. A positive exponent (8 in this case) means the decimal point is to be moved to the right.
03

Move the Decimal Point

Move the decimal point 8 places to the right. Starting with 5.5, moving the decimal point 8 places to the right fills in with zeros as needed:\[5.5 \rightarrow 550000000\]
04

Write the Final Answer

After moving the decimal point 8 places to the right, the number in decimal form is:\[550000000\]

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Key Concepts

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

decimal form
The concept of 'decimal form' refers to writing numbers using the base-10 system, which is the most common numerical system across the world. When converting from scientific notation to decimal form, your goal is to express the number as a simple, non-exponential form. For example, when we have the number \(5.5 \times 10^{8}\), we aim to move the decimal point 8 places to the right to get the decimal form. This results in the number 550,000,000 in decimal form. Decimal form is straightforward and easy to comprehend, particularly for everyday applications like counting money or measuring quantities.
exponentiation
Exponentiation is a mathematical operation involving two numbers, the base and the exponent. In our exercise, the base is 10 and the exponent is 8, written as \(10^8\). The exponent tells us how many times to multiply the base by itself. In this case, 10 multiplied by itself 8 times is: \[10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 = 100000000\]. When you multiply a number by \(10^8\), what you are doing is moving the decimal point 8 places to the right, converting \5.5\ into 550,000,000. This process highlights the power of exponentiation in simplifying and expressing very large or very small numbers compactly.
place value
Place value is a fundamental concept in understanding numbers. It tells us the value of a digit based on its position in a number. For instance, in the number 550,000,000, each digit has a specific place value. Starting from the right, the first digit is in the 'ones' place, the next is in the 'tens' place, and so on. The zeros are crucial as they help position the non-zero digit in its correct place value. Moving the decimal point 8 places to the right in our initial number \(5.5\) means we add enough zeros to fill in the place values up to 100 million, effectively demonstrating the importance of each digit's position in the final representation of the number.

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