When multiplying two numbers in scientific notation, what operations do you use on the coefficients and the exponents of the powers of 10?
When multiplying two numbers in scientific notation, you multiply the coefficients and add the exponents of the powers of 10.
For example, consider the numbers 2.5 x 10^3 and 3.2 x 10^2.
To multiply these two numbers, you would multiply the coefficients (2.5 x 3.2 = 8) and add the exponents of the powers of 10 (3 + 2 = 5). Hence, the product of these two numbers in scientific notation would be 8 x 10^5.
When multiplying two numbers in scientific notation, you perform the following operations on the coefficients and the exponents:
1. Multiply the coefficients: Multiply the numbers without the powers of 10.
2. Add the exponents: Add the exponents in the powers of 10.
3. Adjust the resulting number: If necessary, convert the number back to scientific notation, ensuring that the coefficient is between 1 and 10 (inclusive) and the exponent is adjusted accordingly.
To summarize:
- Multiply the coefficients
- Add the exponents
- Adjust the resulting number to scientific notation if needed.
When multiplying two numbers in scientific notation, you need to perform two separate operations: multiplication of the coefficients and addition of the exponents.
Here's how to do it step by step:
1. Multiply the coefficients: Multiply the numerical parts (coefficients) of the two numbers together, just as you would in regular multiplication.
2. Add the exponents: Add the exponents (powers of 10) of the two numbers together. This accounts for the "shifting" of the decimal point, which occurs when multiplying two numbers in scientific notation.
3. Adjust the result: If the product of the coefficients is greater than or equal to 10, you should adjust it by moving the decimal point to the left and increasing the exponent by 1. This ensures that the result is expressed in proper scientific notation.
Let's illustrate this with an example:
Example:
Multiply (2.5 x 10^4) and (3.0 x 10^2)
Step 1: Multiply the coefficients:
2.5 x 3.0 = 7.5
Step 2: Add the exponents:
10^4 + 10^2 = 10^(4+2) = 10^6
Step 3: Adjust the result:
7.5 is already in the proper format, so no adjustment is needed.
The final answer is 7.5 x 10^6.
Remember to follow these steps whenever multiplying numbers in scientific notation to ensure you obtain the correct result.