Chem 2.3 - Using Scientific Measurements
|How many significant figures are in the number 20?||1|
|How many significant figures are in the number 20. ?||2 (the decimal place makes the zero significant)|
|How many significant figures are in the number 20.0 ?||3|
|How many significant figures are in the number 0.04604 ?||4|
Trailing zero: Counts as a significant figure if the number contains a decimal point. However, it does not count if the number does not contain a decimal point. Example: 50.00 (4 significant figures), 50 (1 significant figure), 50. (2 significant figures).
so 1000. is our four-significant-figure answer. (from rules 5 and 6, we see that in order for the trailing zeros to "count" as significant, they must be followed by a decimal. Writing just "1000" would give us only one significant figure.)
c) Trailing zeros are zeros at the right end of the number. Trailing zeros are only significant if the number contains a decimal point. For example, the number 200 has only one significant figure, while the number 200. has three, and the number 200.00 has five significant figures.
There are three rules on determining how many significant figures are in a number: Non-zero digits are always significant. Any zeros between two significant digits are significant. A final zero or trailing zeros in the decimal portion ONLY are significant.
The following rule applies for multiplication and division: The LEAST number of significant figures in any number of the problem determines the number of significant figures in the answer.
Leading zeros are not significant. For example, 0.00052 has two significant figures: 5 and 2. Trailing zeros in a number containing a decimal point are significant. For example, 12.2300 has six significant figures: 1, 2, 2, 3, 0 and 0.
Rules for Numbers WITHOUT a Decimal Point
- START counting for sig. figs. On the FIRST non-zero digit.
- STOP counting for sig. figs. On the LAST non-zero digit.
- Non-zero digits are ALWAYS significant.
- Zeroes in between two non-zero digits are significant. All other zeroes are insignificant.
How does sig figs checking work?
|1234||=||4 significant figures|
|500||=||1 significant figure|
|500.||=||3 significant figures|
|1300||=||2 significant figures|
|2.000||=||4 significant figures|
Zeroes placed before other digits are not significant; 0.046 has two significant digits. Zeroes placed between other digits are always significant; 4009 kg has four significant digits. Zeroes placed after other digits but behind a decimal point are significant; 7.90 has three significant digits.
Zero is not "nothing", zero is also not the absence of value, zero is a value. You can say that you have 3 objects (apples, bananas, cars, etc), but you can never have 3. 3 is a concept that does not "exist" in reality. It is simply a language used to describe dimensions of real objects.
The trailing zeros do not count as significant. Trailing zeros in a number containing a decimal point are significant. For example, 12.2300 has six significant figures: 1, 2, 2, 3, 0, and 0. The number 0.000122300 still has only six significant figures (the zeros before the 1 are not significant).
3. Trailing zeros in a number are significant only if the number contains a.
Example: 100.0 has 4 significant figures.
Example: 100.0 has 4 significant figures.
Most exact numbers are integers: exactly 12 inches are in a foot, there might be exactly 23 students in a class. Exact numbers are often found as conversion factors or as counts of objects. Exact numbers can be considered to have an infinite number of significant figures.
Exact numbers are those that have defined values or are integers that result from counting numbers of objects. For example, by definition, there are exactly 12 eggs in a dozen, exactly 1000 g in a kilogram, and exactly 2.54 cm in an inch.
Intermediate calculations are truncated; intermediate steps and final answers are rounded. An intermediate calculation is any math function within a formula. An intermediate step is the value that is carried forward into another calculation.
(When you ask for seating in a restaurant, the number of people is an integer, an exact number.) Measured numbers are an estimated amount, measured to a certain number of significant figures without the benefit of any natural unit or numbers that come from a mathematical operation such as averaging.
If you do arithmetic with exact numbers (and they aren't too large) the answer that you get back is exactly right. In Maple, rational numbers (integers and fractions) are exact. If you do arithmetic with rational numbers, your answer will be correct to the last digit. Here are some examples.
No number can claim more fame than pi. Defined as the ratio of the circumference of a circle to its diameter, pi, or in symbol form, π, seems a simple enough concept. But it turns out to be an "irrational number," meaning its exact value is inherently unknowable.
Exact and inexact numbers. Numbers are of two kinds: exact and inexact. An exact number has a value that has no uncertainty associated with it. Exact numbers occur in definitions, in counting, and in simple fractions. An inexact number has a value that has a degree of uncertainty associated with it.