Express this number in scientific notation. 0.5401 – Scientific notation is a powerful tool for representing very large or very small numbers in a concise and manageable form. In this article, we will explore the basics of scientific notation and demonstrate how to express the number 0.5401 using this notation.
Scientific notation consists of two parts: the mantissa and the exponent. The mantissa is the significant digits of the number, and the exponent is the power of 10 by which the mantissa is multiplied. For example, the number 6.022 x 10^23 represents the mantissa 6.022 multiplied by 10 raised to the power of 23.
Scientific Notation
Scientific notation is a method of expressing numbers that are very large or very small in a compact and convenient way. It is used in a wide variety of fields, including science, engineering, and mathematics.
Scientific notation consists of two parts: a mantissa and an exponent. The mantissa is the number that is multiplied by the exponent. The exponent is a power of 10 that indicates how many times the mantissa is multiplied by 10.
For example, the number 6.022 x 10 23is written in scientific notation. The mantissa is 6.022 and the exponent is 23. This means that the number is equal to 6.022 x 10 x 10 x 10 x … x 10 (23 times).
Converting Numbers to Scientific Notation
To convert a number to scientific notation, follow these steps:
- Move the decimal point 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.
- The mantissa is the number that is left after the decimal point was moved.
- The exponent is the number of places the decimal point was moved, but with the opposite sign.
For example, to convert the number 12345 to scientific notation, we would move the decimal point 4 places to the left, giving us 1.2345. The mantissa is 1.2345 and the exponent is -4.
Expressing 0.5401 in Scientific Notation, Express this number in scientific notation. 0.5401
To express 0.5401 in scientific notation, we would move the decimal point 3 places to the left, giving us 5.401. The mantissa is 5.401 and the exponent is -3.
Therefore, 0.5401 in scientific notation is 5.401 x 10 -3.
Examples and Applications
Here are some additional examples of converting numbers to scientific notation:
- 12345 = 1.2345 x 10 4
- 0.00012345 = 1.2345 x 10 -5
- 602200000000000000000000000000 = 6.022 x 10 23
Scientific notation is used in a wide variety of applications, including:
- Astronomy: to express the distances to stars and galaxies
- Chemistry: to express the concentrations of chemicals
- Physics: to express the sizes of atoms and subatomic particles
| Number | Scientific Notation |
|---|---|
| 12345 | 1.2345 x 104 |
| 0.00012345 | 1.2345 x 10-5 |
| 602200000000000000000000000000 | 6.022 x 1023 |
FAQs: Express This Number In Scientific Notation. 0.5401
What is the purpose of scientific notation?
Scientific notation allows us to represent very large or very small numbers in a concise and manageable form, making it easier to perform calculations and communicate numerical data.
How do I convert a number to scientific notation?
To convert a number to scientific notation, move the decimal point to the right or left until there is only one non-zero digit to the left of the decimal point. The exponent of 10 is the number of places the decimal point was moved.
The mantissa is the resulting number with the decimal point moved.
