Writing in Scientific Notation

Scientific notation simplifies the representation of very large or small numbers, making them easier to compare, read, and calculate. To write a number in scientific notation, follow these steps:

1. Locate the original decimal's position.
2. Determine if the number is greater than or equal to 1, but less than 10.
3. Move the decimal to obtain a number between 1 and 10, keeping track of the number of decimal places moved.
4. Multiply the decimal number by the appropriate power of 10 obtained by counting the decimal places moved.

Converting to Scientific Notation

To convert a number to scientific notation, follow these rules:

• If the number is greater than or equal to 1, but less than 10, no change is required.
• If the number is less than 1, move the decimal to the right, making sure to keep track of the number of decimal places moved.
• Multiply the new decimal number by the appropriate power of 10 obtained by counting the decimal places moved.

Operations with Scientific Notation

Scientific notation follows the same rules for addition, subtraction, multiplication, and division as any other number system. To perform operations:

• Treat the decimal parts as usual.
• For the exponents, follow these general rules:
  • For addition and subtraction of exponents, keep the base the same and add or subtract the exponents.
  • For multiplication, add the exponents.
  • For division, subtract the exponent of the divisor from the exponent of the dividend.

Comparing Numbers in Scientific Notation

Comparing numbers in scientific notation is simple because the exponents indicate the relative magnitude of the numbers. A larger exponent indicates a larger number, while a smaller exponent indicates a smaller number.

Example:

• To compare (1.2 \times 10^5) and (3.45 \times 10^6), you would notice that (10^6) is more than (10^5), meaning (3.45 \times 10^6) is larger than (1.2 \times 10^5).

Confidence: 95%