when multiplying two numbers in scientific notation what operations do you use on the coefficients

Answer 1

When multiplying two numbers in scientific notation, you follow these steps:

1. Multiply the coefficients: You take the numerical parts (the coefficients) of the scientific notation and multiply them together.

2. Add the exponents: You add the exponents of the powers of ten together.

The general formula for multiplying two numbers in scientific notation can be expressed as:

If \( a \times 10^m \) and \( b \times 10^n \) are in scientific notation, then their product is:

\[ (a \times b) \times 10^{(m+n)} \]

Example:

Let’s multiply \( 3.0 \times 10^4 \) and \( 2.0 \times 10^3 \).

1. Multiply the coefficients: \[ 3.0 \times 2.0 = 6.0 \]

2. Add the exponents: \[ 4 + 3 = 7 \]

Putting it together, the product is: \[ 6.0 \times 10^7 \]

So, \( (3.0 \times 10^4) \times (2.0 \times 10^3) = 6.0 \times 10^7 \).