lain how to add, subtract, multiply, and divide in scientific notation.

Answer 1

To perform operations such as addition, subtraction, multiplication, and division with numbers written in scientific notation, you need to follow a few guidelines. Here's how to do each operation:

1. Addition/Subtraction:
- First, ensure that the numbers being added or subtracted have the same exponent (power of 10). If they don't, convert one or both numbers so that they have matching exponents.
- Once the exponents are the same, simply add or subtract the coefficients (the numbers in front of the powers of 10).
- Keep the resulting sum or difference in scientific notation by representing it in the form A × 10^B, where A is a number between 1 and 10 (coefficient), and B is the exponent.

Example:
Let's add two numbers in scientific notation: 2.5 × 10^4 and 3.6 × 10^3.
- To match the exponents, convert 3.6 × 10^3 to scientific notation with an exponent of 4: 0.36 × 10^4.
- Now, add the coefficients: 2.5 + 0.36 = 2.86.
- Write the answer in scientific notation: 2.86 × 10^4.

2. Multiplication:
- Multiply the coefficients of the numbers and add their exponents to find the new exponent.
- Adjust the mantissa (coefficient) if necessary so that it remains a number between 1 and 10.
- Express the result in scientific notation.

Example:
Let's multiply two numbers in scientific notation: 2.5 × 10^4 and 3.6 × 10^3.
- Multiply the coefficients: 2.5 × 3.6 = 9.
- Add the exponents: 4 + 3 = 7.
- Adjust the mantissa (if needed) so it remains between 1 and 10: 9 can stay as it is.
- Express the answer in scientific notation: 9 × 10^7.

3. Division:
- Divide the coefficients of the numbers and subtract their exponents to find the new exponent.
- Adjust the mantissa (coefficient) if necessary so it remains between 1 and 10.
- Express the result in scientific notation.

Example:
Let's divide two numbers in scientific notation: 2.5 × 10^4 by 3.6 × 10^3.
- Divide the coefficients: 2.5 ÷ 3.6 ≈ 0.6944 (rounded to four decimal places).
- Subtract the exponents: 4 - 3 = 1.
- Adjust the mantissa (if needed) so it remains between 1 and 10: 0.6944 is already between 1 and 10.
- Express the answer in scientific notation: 0.6944 × 10^1.

Remember to always represent the final answer in scientific notation format (A × 10^B) to maintain the characteristics of numbers in scientific notation.