Understanding Scientific Notation

Scientific notation is a way of writing very large or very small numbers in a more compact and manageable form. It's expressed as a number between 1 and 10 (the coefficient) multiplied by a power of 10. For instance, the number 5,800,000 can be written as 5.8 x 10⁶. Here, 5.8 is the coefficient, and 6 is the exponent. Similarly, a very small number like 0.000043 is written as 4.3 x 10⁻⁵. The key is to move the decimal point until you have a number between 1 and 10, and the number of places you moved the decimal becomes the exponent of 10. If you move the decimal to the left, the exponent is positive; if you move it to the right, the exponent is negative.

Calculations with Scientific Notation
Performing calculations with numbers in scientific notation is straightforward. When multiplying, you multiply the coefficients and add the exponents. For example, (2 x 10³) * (3 x 10⁴) = (2 * 3) x 10³⁺⁴ = 6 x 10⁷. When dividing, you divide the coefficients and subtract the exponents. For instance, (8 x 10⁷) / (2 x 10⁴) = (8 / 2) x 10⁷⁻⁴ = 4 x 10³.

For addition and subtraction, the exponents on the 10s must be the same. If they aren't, you'll need to adjust one of the numbers. For example, to add (2 x 10³) and (3 x 10⁴), you could rewrite 3 x 10⁴ as 30 x 10³. Then, you can add the coefficients: (2 + 30) x 10³ = 32 x 10³. Finally, you would adjust the answer to be in proper scientific notation, which would be 3.2 x 10⁴.