A significant digit might be defined, simply, as "the accuracy to which something is measured or calculated."
For example, if one was to measure the length of a given object, a rudimentary, "estimated" measurement might end up with a value of 4 meters, at which point the object would have been measured to only one significant digit. A more careful measurement might allow 2 significant digits (4.5 meters), 3 significant digits (4.56), 4 (4.567), or even more (4.5678344543 - eleven significant digits).
The point in this is that the number of significant digits demonstrate the accuracy to which something is either measured or calculated.
Non-significant Digits
A common mistake one might make upon first learning of the importance of significant digits would be to simply count up the numbers in any given value and assume that this is the number of significant digits, but this does not always hold true.
Take, for example, a rather large object, which one might estimate has a length of about 3,000 meters. Even though this number has four digits, it has only one significant digit (3), while the zeros act as "placeholders," existing only to show the distance between the significant digit and the decimal point. A scientist, wanting to avoid confusion, might then write this number as 3 x 10^3. (The "^" symbol means "to the power of...").
In fact, this is one of the primary reasons for the invention of this scientific notation in the first place - to demonstrate the number of significant digits and avoid the confusion of unnecessary zeros.
Of course, one must also not assume that every zero is a mere placeholder, either. Zeros act as significant digits anywhere within the middle of a number (6.04, for example, has three S.D.'s), and can even exist at the end of a number (6.340 x 10^3 implies that this zero is a significant digit, otherwise it would not have been included).
Using Significant Digits
The idea of significant digits truly comes in handy when more than one number is being used in a given problem. Take, for example, the formula for finding an object's average speed: Speed = Distance/Time.
Now, given an object which was observed to have traveled 6.2 kilometers over a period of 104.3 seconds, it is easy to calculate the average speed as being 0.059443911. Wow! That's quite an accurate number!
Unfortunately, this number does not hold up. In physics, one of the first things a person learns is that the answer to a problem should never have more significant digits than the least accurate of the original elements. The truth is that the question truly only allows for an answer with, two significant digits (because the measurement for distance only had 2 significant digits, so the answer cannot be more exact than this), which gives an answer of 0.059.
Learning this basic mathematical idea is essential for understanding the do's and don’ts of both math and physics, and for avoiding those potential pitfalls which stem from a misunderstanding of mathematical accuracy.
Isaac M. McPhee - Isaac McPhee was born as a human child in Mt. Vernon, WA, c. 1982; he currently resides in the bustling heart of New York City where he ...
