×10^n

Definition

The term '×10^n' is a mathematical notation used to represent numbers in scientific notation, where 'n' is an integer exponent. This notation allows for the concise expression of very large or very small numbers by scaling the base number 10 by a power of 10.

5 Must Know Facts For Your Next Test

1. The '×10^n' notation is used to represent numbers in scientific notation, which is a way of expressing very large or very small numbers in a more compact and manageable form.
2. The exponent 'n' in '×10^n' indicates the number of places the decimal point needs to be moved to the right (for positive exponents) or to the left (for negative exponents) to express the original number.
3. When the exponent 'n' is positive, the value represented by '×10^n' is a large number, and when 'n' is negative, the value is a small number.
4. The base number '10' is used because it is the most common and convenient base for scientific notation, as it corresponds to the decimal number system.
5. Proficiency in understanding and working with '×10^n' notation is essential for manipulating and interpreting numbers in scientific and mathematical contexts.

Review Questions

• Explain how the '×10^n' notation is used to represent numbers in scientific notation.
  • The '×10^n' notation is used to represent numbers in scientific notation, which is a way of expressing very large or very small numbers in a more compact and manageable form. The exponent 'n' indicates the number of places the decimal point needs to be moved to the right (for positive exponents) or to the left (for negative exponents) to express the original number. For example, the number 5,000 can be written as 5 × 10^3, and the number 0.000005 can be written as 5 × 10^-6.
• Describe how the value represented by '×10^n' changes depending on the sign of the exponent 'n'.
  • The value represented by '×10^n' is directly related to the sign of the exponent 'n'. When the exponent 'n' is positive, the value represented by '×10^n' is a large number, as the base number 10 is multiplied by itself 'n' times, resulting in a value greater than 1. Conversely, when the exponent 'n' is negative, the value represented by '×10^n' is a small number, as the base number 10 is divided by itself 'n' times, resulting in a value less than 1.
• Explain the significance of using the base number '10' in the '×10^n' notation and how it relates to the decimal number system.
  • The base number '10' is used in the '×10^n' notation because it is the most common and convenient base for scientific notation, as it corresponds to the decimal number system. The decimal number system is based on the use of 10 digits (0-9), and the '×10^n' notation allows for the easy conversion between standard decimal notation and scientific notation. This makes it easier to work with and interpret very large or very small numbers in scientific and mathematical contexts, as the '×10^n' notation provides a standardized way to express the magnitude or scale of a value.

Related terms

Scientific Notation: A way of writing numbers that uses powers of 10 to indicate the scale or magnitude of a value, making it easier to work with very large or very small numbers.

Exponential Notation: A way of expressing a number as a base number multiplied by a power of that base, such as 5 × 10^3 to represent the number 5,000.

Integer Exponents: Exponents that are whole numbers, either positive or negative, used to represent the power to which a base number is raised.