University:
University of Arkansas
Course:
CHEM 1053 | Chemistry in the Modern World
Academic year:

2023
Views:

367

Pages:

1
Author:

madeleinejames20

To determine the number of significant figures in a measurement, we apply four rules for significant figures. The first rule is that all non-zero digits are significant. So when the number is 28.03, the 2, 8, and 3 are significant. To determine if the zero is significant in this number, we need to apply another rule. Our second rule is that interior zeros, which are between two non-zero digits, are significant. So in the number 35.008, there are five significant figures, and in the number 305.09, we also have five significant figures. Our third rule is that leading zeros, which occur to the left of the first non-zero digit, are not significant. These zeros are only placeholders. So in the number 0.0000389, we only have three significant figures. Trailing zeros are to the right of the last non-zero digit. There are three possibilities for trailing zeros. If the trailing zero occurs after a decimal point, it is significant. So the number 2.0 has two significant figures. If the trailing zero occurs before an explicit decimal point, it is also significant. So the number 150.0 has four significant figures. But if a trailing zero occurs before an implied decimal point, it is ambiguous. This means we don't know if it is significant or not significant. For example, if we have the number 1200 without an explicit decimal point, we don't know how many significant figures are in the measurement. The measurement could have been taken with an instrument that could tell the difference only between 1000 and 2000, so that the hundreds digit was estimated. Or the measurement could've been taken with an instrument that could tell the difference between 1200 and 1300, so that the tens digit was estimated. Or the measurement could have been taken with an instrument that could tell the difference between 1200 and 1210, so that the ones digit was estimated. We simply don't know. To avoid this ambiguity, we report the number in scientific notation. For example, if we reported it as 1.2 times 10 to the third, we would have two significant figures. Or if we reported it as 1.200 times 10 to the third, we would have four significant figures. Scientific notation consists of a coefficient which is multiplied times 10 raised to an integer exponent. In standard scientific notation, the coefficient is one or greater and less than 10. With scientific notation, we can report numbers that are very large or very small much more conveniently, and we can easily indicate exactly how many of our digits are significant.