What does significant mean? It means the numbers that are important.
How do you determine which ones are important? Use the table below.
1. All nonzero digits of a measurement are significant.
Ex. If a balance reads 283.47g then all numbers are significant.
2. Zeros occurring between significant numbers are significant
Ex. The balance reads 50.63 g then all four numbers are significant.
3. All final zeros past the decimal point are significant
73.00 grams means that you have 73.00 grams, not just 73 grams.
It is much more precise, and therefore significant
4. Zeros used as placeholders are NOT significant.
“300” has one significant number, “3”. The zeros just hold the place of the three. By writing “300” in scientific notation you can get rid of the zeros – 3 x 102. If you indeed have 300 grams or 300 people that you counted you can make the zeros significant by writing – 3.00 x 102.
Adding and Subtracting significant numbers.
The Key: The answer is only as precise as the measurement that is the least precise.
Ex. 190.2 g 309.567 ml
265.291 g - 7.2 ml
+12.38 g 305.367 ml
Answer Rounded to 467.9 g Answer rounded to 305.4 ml
Following the key above, both are rounded to the nearest tenths place because the tenths place is the least precise measurement in both problems.
Multiplying and Dividing significant numbers.
The Key: The answer has only as many significant digits as the measurement with the least number of significant digits.
Ex. 13.78 g 3.2 g
11.3 ml x 6.022
The answer on the left is rounded to 1.22 g/ml because the least number of significant digits in the problem is three. The answer on the right is rounded to 19 g because the least number of digits in the problem is two.