In science, we often use very large or very small numbers. To make these easier to present, scientists use scientific notation, which multiplies a number (called the coefficient) by 10 (the base) raised to a given power (the exponent). If the coefficient is 1, we can leave it off and simply show the base and exponent (e.g. 1 × 102 = 102). The exponent tells us how many orders of magnitude larger or smaller to make the number. In other words, the exponent is telling us how many zeros the number will have: 102 = 100; 103 = 1,0 00, and so on. Negative exponents represent decimals; for example: 10–2 = 0.01; 10–3 = 0.001, and so on.
Here is a simple shorthand way to evaluate numbers given in scientific notation. Move the decimal place to the right if 10 has a positive exponent, and to the left if the exponent is negative. The number of spaces the decimal place is moved is equal to the exponent. For example, 102 tells us to move the decimal place 2 spaces to the right; 10–2 means we move it 2 spaces to the left.
By convention, we always designate the coefficient as a whole number (2) or a decimal, with the decimal point at the “10” position (2.3). In other words we would write 2.3 × 105, not 23 × 104. Both are technically correct but the first is the preferred format.
Examples:
2 × 106 = 2,000,000
2.36 × 105 = 236,000
4.99 × 10–4 = 0.000499
Some typical values you might run across include:
106 = 1 million
109 = 1 billion
1012 = 1 trillion
A-3