Significant Digit Rules
1. All non-zero numbers are significant Example: 157 has 3 sigs
2. All zeros between two significant digits are significant Example: 1007 has 4 sigs
3. Leading zeros BEFORE an integer are NOT significant Ex. 0.005 has 1 sig
4. Zeros FOLLOWING an integer are NOT significant Ex. 5000 has 1 sig
5. A decimal placed after a zero make it significant Ex. 5000. Has 4 sigs
6. All numbers in scientific notation are significant Ex. 370000 x 107 has 6 sigs
7. A final zero AFTER a decimal point is significant Ex. 700.00 has 5 sigs
What is the difference between a “significant” digit and an “important” digit?
The best way for me to explain this is by using money as the example. This is something that everyone understands.
Let us assume that we know of a famous millionaire. We know from the newspaper that she is worth 6 million dollars! We could write this: $6,000,000
But, if you were to look at her actual bank account, would you really expect it to be 6 million dollars to the penny? Of course not! In fact, I happen to know her bank account number and I looked it up. She in fact has: $6,345,291.78 as of today.
The zeros in the 6 million are IMPORTANT but they are not SIGNIFICANT. The “345,291.78” on the other hand, are significant since they really do exist.
If the IMPORTANT zeros weren’t there, then she would be worth 6 lousy bucks! But those zeros don’t tell an accurate enough story about her financial holdings. I’d be happy to have the $345,291.78 of the so called $6 million she has. Wouldn’t you? Heck, I’d settle for the $1.78
But what should we do if she really were worth $6 million to the penny?
$6,000,000. (put a decimal point at the end – see rule #5)
Another silly example for you:
If I told you that I had $700 you’d think I had $700 or close to it.
If I told you that I had $701 you’d know I had that amount and that the zero sandwiched in between the 7 and the 1 was a real “significant” number. (see rule #2)
REMEMBER THIS: Just because a number isn’t significant doesn’t mean it isn’t important. We need all those zeros to hold the place value of a number. But the zeros may or may not give us a real value.
How do you use Significant digits when performing calculations?
You can only have the amount of significant digits in your answer as the number with the LEAST number of significant digits in the problem! Think about it. If you add the following numbers together:
Your answer has to be $6,000
WHY? Because you don’t know if that $6,000 figure is accurate or not. The least amount of significant digits in the problem is 1.
What if you added these three numbers (notice the subtle difference)
$6,000. Do you see the decimal point? It increases the sig figs of this number to 4
Your answer has to be $6,022
WHY? Because now the least amount of significant digits in the problem is 4. And, while you might expect an answer of $6,022.39 (which has 6 sig figs) you need to realize that you must round it to 4 significant digits.