When multiplying two numbers in scientific notation, what operations do you use on the coefficients and the exponents of the powers of
To multiply two numbers in scientific notation, you multiply the coefficients and add the exponents.
For example:
Let's say we have 3.4 x 10^5 multiplied by 2.7 x 10^3.
First, multiply the coefficients: 3.4 x 2.7 = 9.18.
Then, add the exponents: 10^5 + 10^3 = 10^8.
So the result in scientific notation is 9.18 x 10^8.
When multiplying two numbers in scientific notation, you perform the following operations on the coefficients and exponents:
1. Multiply the coefficients (the numbers in front of the powers of 10).
2. Add the exponents (powers of 10) together.
For example, let's say you have:
Number 1: 2.5 x 10^3
Number 2: 4.7 x 10^2
To multiply these two numbers:
Step 1: Multiply the coefficients: 2.5 x 4.7 = 11.75
Step 2: Add the exponents: 10^3 + 10^2 = 10^5
The result is 11.75 x 10^5 in scientific notation.
When multiplying two numbers in scientific notation, you need to perform the following operations on the coefficients and the exponents of the powers of 10:
1. Multiply the coefficients: Multiply the two numbers without considering the exponents. This gives you the product of the two coefficients.
2. Add the exponents: Add the exponents of the two numbers. This gives you the new exponent for the product.
3. Adjust the result: If the product of the coefficients is greater than or equal to 10, you need to adjust the result. Move the decimal point to the left by one position and increase the exponent by 1.
To summarize, the steps for multiplying numbers in scientific notation are:
- Multiply the coefficients.
- Add the exponents.
- Adjust the result if necessary.
Let me give you an example to illustrate this:
Example:
Let's multiply 3.2 x 10^4 and 4.5 x 10^2.
Step 1: Multiply the coefficients: 3.2 x 4.5 = 14.4.
Step 2: Add the exponents: 10^4 + 10^2 = 10^6.
Step 3: Adjust the result: The product 14.4 is less than 10, so no adjustment is needed.
Therefore, the product of 3.2 x 10^4 and 4.5 x 10^2 is 14.4 x 10^6.