Multiplying with Scientific Notation

 

Multiplying numbers in scientific notation follows a straightforward process. Here’s a step-by-step guide:

Step 1: Write the numbers in scientific notation

Ensure both numbers are in the proper scientific notation format. This means the number is written as $a \times 10^n$, where:

• $a$ is a number between 1 and 10 (a decimal).
• $n$ is an integer (the exponent of 10).

Example:

• $(3.2 \times 10^4)$ and $(4.5 \times 10^3)$.

Step 2: Multiply the decimal parts

Multiply the coefficients (the numbers in front of the $\times 10^n$).

Step 3: Add the exponents

Add the exponents of 10. When multiplying, you add the exponents.

Step 4: Combine the results

Now, combine the product of the decimal parts and the result of the exponent addition.

Step 5: Adjust the result if needed

If the coefficient (the decimal part) is not between 1 and 10, adjust it:

• If you move the decimal point to the left the number gets smaller and the exponents needs to get larger. You will add to the exponent the number of places you move the decimal.

• If you move the decimal point to the left the number gets larger and the exponents needs to get smaller. You will add to the exponent the number of places you move the decimal.

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