key term - Mantissa

Definition

The mantissa is the fractional part of a logarithm or a number expressed in scientific notation. It represents the significant digits of a number and is a crucial component in understanding the properties of exponents and working with scientific notation.

5 Must Know Facts For Your Next Test

1. The mantissa is the part of a number that comes after the decimal point in scientific notation.
2. The mantissa determines the precision and significant digits of a number expressed in scientific notation.
3. When working with exponents, the mantissa is used to represent the base number, while the exponent represents the power to which the base is raised.
4. Manipulating the mantissa is crucial in performing operations with numbers in scientific notation, such as multiplication, division, and raising to a power.
5. The mantissa can range from 1.00 to 9.99, and the exponent adjusts the magnitude of the number accordingly.

Review Questions

• Explain the role of the mantissa in the context of scientific notation.
  • The mantissa in scientific notation represents the significant digits of a number. It determines the precision and accuracy of the number by specifying the part of the number that is not zero. The mantissa, along with the exponent, allows for the efficient representation of very large or very small numbers. The mantissa is the fractional part of the number, while the exponent indicates the power of 10 by which the mantissa is multiplied.
• Describe how the mantissa is used in operations with numbers in scientific notation.
  • When performing operations such as multiplication, division, or raising to a power with numbers in scientific notation, the mantissa plays a crucial role. The mantissa represents the base number, while the exponent represents the power. To multiply or divide numbers in scientific notation, you manipulate the mantissas and add or subtract the exponents, respectively. When raising a number in scientific notation to a power, you multiply the mantissa by the power and add the product of the exponent and the power. The mantissa ensures the proper representation of significant digits throughout these operations.
• Analyze the relationship between the mantissa and the properties of exponents in the context of scientific notation.
  • The mantissa and the properties of exponents are deeply interconnected in the realm of scientific notation. The mantissa represents the significant digits of a number, while the exponent indicates the magnitude or power of 10 by which the mantissa is multiplied. When working with exponents, the mantissa is used to represent the base number, and the exponent represents the power to which the base is raised. This relationship allows for the efficient manipulation of numbers in scientific notation, as the mantissa and exponent can be adjusted independently to perform operations such as multiplication, division, and raising to a power. Understanding the role of the mantissa is crucial in applying the properties of exponents to numbers expressed in scientific notation.

Related terms

Exponent:

The exponent is the power to which a base number is raised, indicating the number of times the base is multiplied by itself.

Scientific Notation:

Scientific notation is a way of expressing very large or very small numbers by using exponents of 10 to represent the magnitude of the number.

Characteristic: The characteristic is the integer part of a logarithm or the exponent in the scientific notation representation of a number.