E Notation

Definition

E notation, also known as scientific notation, is a compact way of writing very large or very small numbers. It uses the letter 'E' (or sometimes 'e') to represent the power of 10 by which the number is multiplied, allowing for efficient representation of numbers that would otherwise be cumbersome to write out in full.

5 Must Know Facts For Your Next Test

1. E notation is particularly useful for expressing very large or very small numbers, as it allows for a more concise representation.
2. The number before the 'E' is called the mantissa, and the number after the 'E' is the exponent, which represents the power of 10.
3. E notation can be used to perform calculations more efficiently, as the exponent can be easily manipulated.
4. Converting between standard form and E notation involves moving the decimal point to the right (for positive exponents) or left (for negative exponents) by the number of places indicated by the exponent.
5. E notation is widely used in scientific and technical fields, such as physics, chemistry, and engineering, where dealing with very large or very small numbers is common.

Review Questions

• Explain how E notation is used to represent very large or very small numbers.
  • E notation, or scientific notation, is a compact way of writing numbers that are extremely large or extremely small. It uses the letter 'E' (or 'e') to represent the power of 10 by which the number is multiplied. The number before the 'E' is called the mantissa, and the number after the 'E' is the exponent, which indicates the scale or order of magnitude of the number. For example, the number 6,000,000 can be written as 6E6 or 6e6, and the number 0.000000045 can be written as 4.5E-8 or 4.5e-8. This allows for efficient representation of numbers that would otherwise be cumbersome to write out in full.
• Describe the process of converting between standard form and E notation.
  • To convert a number from standard form to E notation, the decimal point is moved to the right (for positive exponents) or left (for negative exponents) by the number of places indicated by the exponent. The mantissa is the number that remains to the left of the 'E,' and the exponent is the power of 10 to which that number is raised. For example, to convert 4,560 to E notation, the decimal point is moved 3 places to the left, resulting in 4.56E3. Conversely, to convert 6.02E23 to standard form, the decimal point is moved 23 places to the right, resulting in 602,000,000,000,000,000,000,000.
• Explain the significance of E notation in scientific and technical fields, and how it facilitates calculations and comparisons.
  • E notation is widely used in scientific and technical fields because it allows for the efficient representation of very large or very small numbers. This is particularly important in fields such as physics, chemistry, and engineering, where dealing with quantities that span several orders of magnitude is common. E notation facilitates calculations by allowing the exponent to be easily manipulated, making it easier to perform operations like multiplication and division. Additionally, the use of E notation makes it easier to compare and interpret the scale of different quantities, as the exponent directly indicates the order of magnitude. This helps scientists and engineers to quickly grasp the relative size or significance of different measurements or values, which is crucial for analysis, decision-making, and effective communication of results.

Related terms

Exponents:

Exponents represent the power to which a number is raised, indicating repeated multiplication of the base number.

Significant Figures:

Significant figures are the meaningful digits in a number, used to indicate the precision and accuracy of a measurement or calculation.

Order of Magnitude:

The order of magnitude refers to the scale or size of a quantity, often expressed as a power of 10 that approximates the value.