The given number, 1.207 x 10^7, represents a value in scientific notation. To understand this number, it's essential to break down its components. The coefficient, 1.207, is a decimal number between 1 and 10, and the exponent, 10^7, indicates the power of 10 to which the coefficient should be raised.
Understanding Scientific Notation
Scientific notation is a concise way to express very large or very small numbers. It consists of a number between 1 and 10, multiplied by a power of 10. This notation is widely used in science, engineering, and mathematics to simplify complex calculations and to make it easier to compare numbers of vastly different scales.
Converting to Standard Notation
To convert 1.207 x 10^7 to standard notation, we need to multiply the coefficient by 10 raised to the power of 7. This results in 1.207 x 10,000,000, or 12,070,000. This conversion helps to illustrate the magnitude of the number, making it clearer that we are dealing with a value in the millions.
| Notation | Value |
|---|---|
| Scientific Notation | 1.207 x 10^7 |
| Standard Notation | 12,070,000 |
Applications of Large Numbers
Numbers like 1.207 x 10^7 have numerous applications in real-world scenarios. For instance, in astronomy, the distances between stars and galaxies are often measured in millions or billions of kilometers. In biology, the number of cells in the human body or the number of species on Earth can also be expressed in millions or billions.
Calculation Examples
When working with numbers in scientific notation, it’s essential to follow the rules of exponentiation. For example, to multiply two numbers in scientific notation, we multiply the coefficients and add the exponents. To divide, we divide the coefficients and subtract the exponents.
For example, if we want to calculate the product of 1.207 x 10^7 and 2.5 x 10^3, we first multiply the coefficients (1.207 * 2.5) to get 3.0175, and then add the exponents (7 + 3) to get 10. The result is 3.0175 x 10^10.
| Operation | Example | Result |
|---|---|---|
| Multiplication | (1.207 x 10^7) * (2.5 x 10^3) | 3.0175 x 10^10 |
| Division | (1.207 x 10^7) / (2.5 x 10^3) | 0.4828 x 10^4 |
What is the purpose of scientific notation?
+Scientific notation is used to express very large or very small numbers in a concise and manageable form, making it easier to perform calculations and comparisons.
How do you convert a number from scientific notation to standard notation?
+To convert from scientific notation to standard notation, multiply the coefficient by 10 raised to the power of the exponent. For example, 1.207 x 10^7 becomes 12,070,000.
In conclusion, understanding numbers like 1.207 x 10^7 and their representation in scientific notation is vital for a wide range of applications. By grasping the concepts of scientific notation, conversion between notations, and performing calculations with these numbers, individuals can better comprehend and work with the vast scales found in various scientific and engineering disciplines.
