multiply scientific notation quick check

Answer 1

To multiply numbers in scientific notation, you can follow these steps:

1. Multiply the coefficients: Multiply the numbers in front of the powers of ten (the coefficients).
2. Add the exponents: Add the exponents of the powers of ten.

The general formula is:

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

Example

Multiply \((3 \times 10^4)\) and \((2 \times 10^3)\):

1. Multiply the coefficients: \[ 3 \times 2 = 6 \]

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

So, \((3 \times 10^4) \times (2 \times 10^3) = 6 \times 10^7\).

Practice Problem

Try multiplying \((5 \times 10^2)\) and \((4 \times 10^5)\):

1. Multiply the coefficients: \[ 5 \times 4 = 20 \]

2. Add the exponents: \[ 2 + 5 = 7 \]

So the answer is: \[ 20 \times 10^7 \]

Note: \(20 \times 10^7\) can be converted to proper scientific notation as \(2.0 \times 10^8\) (shifting the power to the right).

Feel free to try another example or let me know if you have any questions!