Express in scientific notation. 472.3 – Expressing 472.3 in scientific notation introduces us to the fascinating world of representing large or small numbers in a concise and efficient manner. Scientific notation, a cornerstone of scientific communication, allows us to express numbers with varying magnitudes in a standardized format, making it easier to perform calculations, compare values, and convey complex data.
This comprehensive guide delves into the intricacies of scientific notation, exploring the concept, its applications, and the specific steps involved in expressing 472.3 in this format. We will also uncover the significance of significant figures and delve into the practical applications of scientific notation across various scientific disciplines.
Expressing 472.3 in Scientific Notation
Scientific notation is a way of expressing very large or very small numbers in a more compact and manageable form. It is commonly used in scientific and engineering fields to represent values that would otherwise be difficult or cumbersome to write in standard notation.
To express 472.3 in scientific notation, we follow these steps:
- Move the decimal point to the left until there is only one non-zero digit to the left of the decimal point.
- Count the number of places the decimal point was moved.
- Write the number in the form a × 10n, where a is the non-zero digit and n is the number of places the decimal point was moved.
In the case of 472.3, the decimal point is moved three places to the left, resulting in the number 4.723. Therefore, 472.3 in scientific notation is expressed as 4.723 × 10 3.
Understanding Significant Figures in 472.3
Significant figures are the digits in a number that are known with certainty. In 472.3, all three digits are known with certainty, so there are three significant figures.
Significant figures are important in scientific notation because they determine the accuracy of the number. When performing calculations with numbers in scientific notation, it is important to consider the number of significant figures in each number to ensure that the result is reported with the correct number of significant figures.
Applications of Scientific Notation: Express In Scientific Notation. 472.3
Scientific notation is used in a wide variety of scientific fields, including:
- Astronomy: To express the distances to stars and galaxies
- Chemistry: To express the concentrations of chemicals
- Physics: To express the masses of atoms and molecules
Scientific notation is also used in engineering and other fields to express very large or very small numbers that would otherwise be difficult or cumbersome to write in standard notation.
Calculations Involving 472.3 in Scientific Notation
| Operation | Result |
|---|---|
| 472.3 + 5.67 × 102 | 6.14 × 102 |
472.3
|
4.49 × 102 |
| 472.3 × 6.54 × 10-3 | 3.08 × 100 |
| 472.3 ÷ 7.89 × 10-2 | 6 × 103 |
- When adding or subtracting numbers in scientific notation, the numbers must have the same exponent.
- When multiplying or dividing numbers in scientific notation, the exponents are added or subtracted, respectively.
Converting Between Standard and Scientific Notation
To convert 472.3 from scientific notation to standard notation, we move the decimal point to the right three places, resulting in the number 4723.
To convert 4723 from standard notation to scientific notation, we move the decimal point to the left three places, resulting in the number 4.723 × 10 3.
Extensions of Scientific Notation
Engineering notation is a variation of scientific notation that is commonly used in engineering and other fields. In engineering notation, the exponent is always a multiple of 3.
For example, 472.3 in engineering notation would be expressed as 4.723 × 10 3.
Engineering notation is used to make it easier to read and write large or small numbers that have many zeros.
Questions Often Asked
What is the purpose of scientific notation?
Scientific notation simplifies the representation of very large or very small numbers, making them easier to read, write, and compare.
How do I express 472.3 in scientific notation?
472.3 = 4.723 x 10^2
What are significant figures?
Significant figures are the digits in a number that are known with certainty, plus one estimated digit.
