Significant figures is simply a technique used in calculations to indicate the precision of the numbers. Three aspects are always involved when there is a measurement:
Accuracy-how close is the reported value to the actual value? You can take an example of π as 3.14, which in the real sense, is 3.142857142857143. The variation between the actual value and the representation is off by 0.05%.
Precision- a measure of how small is the smallest reportable difference. When you say that the distance between two cities is 20 kilometers, you are not precise. However, when you report the same distance to be 20.9876 kilometers, you are exceedingly precise. This measurement shows that your measuring unit is a meter but it is not still very accurate as there are other units of measurement that are lower than that.
Uncertainty- measures the sort of reasonable variation that can be in measurement. Your measurement can never be exact when you take one. It is hard to say how off your measurement is or else you would simply fix it. For instance, you want to measure the diameter of your water pipe using a ruler.
The diameter might fall in the markings between 200mm and 201mm. This implies that the diameter is longer than 200mm but shorter than 201mm. The marking might also be a third way between the two measurements and you can thus say that the diameter is 200.3mm. You can go ahead and give some tenths and estimate it to be between 200.1mm and 200.4mm, which gives ‘take or give 0.2mm’ as the uncertainty.
- Factors that contribute to uncertainty
- What are exact numbers?
- Rules associated with significant figures
- Practical uses
Factors that contribute to uncertainty
- The measuring device’s limitations. For instance, you may end up with the wrong measurements when you have a one-meter ruler, and you want to measure the length of a longer piece of wood. The measurement process may involve taking the measurements a number of times.
- Skills of the person measuring. Some people, like doctors, are more skilled at using a thermometer than an average person who has never attended a medical class.
- Irregularities of the object being measured. For instance, you may find it hard to take the length or diameter of an irregular stone. Some of the objects can only be measured when you use several tools.
- Any other factor that may affect the outcome. For instance, weather variations may affect the mass of objects that absorb moisture. There are also variations in the number of days that make a month.
What are exact numbers?
If you come across a number that is known with complete certainty, then it is an exact number. Most of the exact numbers are integers. For instance, there are exactly 100 centimeters in a meter, 12 inches in a foot and there might be 50 people in a conference. Exact numbers are mostly as a result of conversion or exact counts of certain objects. Such exact numbers have an infinite number of significant figures.
Rules associated with significant figures
Non-zero digits are significant
You can use different devices such as a thermometer, ruler, or triple-beam balance to measure something. The measurement will return a number such as 25.45 or even 2.25. The first measurement will have 4 significant numbers while the second measurement has 3 significant numbers. What about numbers such as 24.07 or 0.000234? This takes us to the second rule.
A zero between 2 significant numbers is significant
When examining a number such as 103 using the first rule, you will conclude that 1 and 3 are significant numbers. 1 is in the hundred’s place while 3 is in the unit’s place. It thus means that you cannot ignore the tenths place. All the 3 numbers in 103 are thus significant.
Trailing zeroes or a final zero in a decimal portion is significant
Take a number like 0.002500. The zero just before the decimal is not significant. The same applies to the zeroes after the decimal point. However, the last two zeroes are significant. The first three zeroes are just space holders, they do not involve any measurement decisions. There are there to avoid confusion. However, the two final zeroes show finality.
Have you ever come across a statement that there were 28,000 people in a football match? That is an estimation of all the people attending the match, and they could have been fewer or more. For instance, there could have been 27,898 people or even 28,002. The estimation here is to give precision based on the next big number. If plans are to be made, then it will be based on the reported number as the variation is not that significant. However, such an estimation cannot be used in a place like a bank. For instance, when you have an outstanding loan of $28,000. Then, it cannot be $27,999 or $28,001. When you pay only $27,999, your statement will indicate that you still owe the bank $1. On the other hand, when you remit $28,001 to your bank, the extra $1 will be credited to your account and can become savings.
Addition and subtraction
In every mathematical operation that involves significant figures, then you will find that the answer is presented in such a way that it reflects the least precise operation’s reliability. To understand this better, you can take the example of a team where all the members must finish together. It thus means that the speed of the slowest member will dictate your overall performance.
Multiplication and division
Multiplying or dividing significant figures applies similar concepts as addition and subtraction. Let us take a real-life example; if you have a saw, the weak link on it will determine how strong the saw will be.
You can now see that significant figures apply to almost all sectors of our life. Understanding the fundamental rules involving significant figures is the first step towards mastering this concept. Luckily, you can use the sig fig calculator right here for all your computations on the same concept.