Scientific Notation Multiplication

Scientific notation multiplication

When multiplying numbers in scientific notation, separate the numbers and the powers of 10.

1) Multiply the coefficients

Multiply the decimal numbers in front. For example, if you have 0a and 0b, compute a d7 b first.

2) Add the exponents

Keep the base 10 and add the powers: [ 10^m \times 10^n = 10^{m+n} ] So the exponent changes by addition, not multiplication.

3) Rewrite in proper scientific notation

After multiplying, check whether the first number is between 1 and 10.

• If it is too large, move the decimal point left and increase the exponent.
• If it is too small, move the decimal point right and decrease the exponent.

4) Check your answer

Your final result should look like [ a \times 10^k ] with (1 \le a < 10). Also, estimate the size of the product to see if the exponent makes sense.

Example structure

If the problem is ((2.4 \times 10^3)(3 \times 10^5)), multiply 2.4 and 3, then add 3 and 5, and finally normalize the result if needed.

A careful decimal check is often the fastest way to avoid mistakes.