Scientific Notation

Definition

Scientific notation is a way of expressing very large or very small numbers in a compact and standardized format. It involves representing a number as a product of a decimal value between 1 and 10, and a power of 10.

5 Must Know Facts For Your Next Test

1. Scientific notation is used to represent extremely large or small numbers in a compact and easily readable format.
2. The decimal value in scientific notation is called the mantissa and must be between 1 and 10, excluding 10 itself.
3. The exponent in scientific notation represents the number of places the decimal point is shifted to the right or left to obtain the original number.
4. Scientific notation simplifies calculations by allowing for easy manipulation of numbers through the use of exponents.
5. Proper use of scientific notation ensures that significant figures are maintained, which is crucial for accurate scientific and mathematical calculations.

Review Questions

• Explain how scientific notation is used to represent very large or very small numbers.
  • Scientific notation is a way of expressing numbers in a compact and standardized format by representing a number as a product of a decimal value between 1 and 10, and a power of 10. This allows for the efficient representation of extremely large or small numbers, as the exponent indicates the number of places the decimal point is shifted. For example, the number 45,000,000 can be written in scientific notation as 4.5 × 10^7, and the number 0.000000045 can be written as 4.5 × 10^-8.
• Describe the relationship between scientific notation and exponential notation.
  • Scientific notation is a specific form of exponential notation, where the base is always 10. In exponential notation, a number is expressed as a product of a decimal value and a power of the base, which can be any number. In scientific notation, the decimal value must be between 1 and 10, excluding 10 itself, and the exponent represents the number of places the decimal point is shifted. This standardized format allows for easy manipulation of numbers through the use of exponents, which is particularly useful in scientific and mathematical calculations.
• Analyze the importance of maintaining significant figures when working with numbers in scientific notation.
  • Maintaining significant figures is crucial when working with numbers in scientific notation, as it ensures the appropriate level of precision and accuracy in calculations. The mantissa, or decimal value, in scientific notation represents the significant figures of the number. By preserving the number of significant figures, you can avoid introducing unnecessary rounding errors or losing important information about the original measurement or value. This is particularly important in scientific and engineering applications, where precise calculations and measurements are essential for making accurate conclusions and decisions.

Related terms

Exponential Notation: A way of expressing numbers using exponents, where the base is 10 and the exponent represents the number of places the decimal point is shifted.

Significant Figures: The meaningful digits in a number, including the first non-zero digit and all other digits deemed important for a particular purpose or calculation.

Standard Form: The default way of writing a number, with the decimal point placed immediately after the first non-zero digit.