What are significant figures?
Significant figures are also known as the significant digits.These are the numbers of digits in a value, often a measurement, that contribute to the degree of accuracy of the value.
We use decimal numbers in measurement. Like 0, 1 , 2, 3, 4, 5, 6, 7, 8, 9. From 1 to 9 ,all are significant figures, it is also called non zeroes digits .But for zero. We have to follow some rules.
Coding OR Rules of Significant Figures:
The Trapped Zeros:
The zeroes which are in between the non-zeroes digits are called trapped zeroes.
Example: 0.01006, there are four significant figures. ‘1006’.
The Leading Zeros:
The zeroes that are at the beginning of the measurement are called Leading zeroes. These zeroes are never significant.
Example: 0.00230, there are 3 significant figures ‘230’.
The zeroes that are in the last of the measurement are called Trailing zeroes.
If the decimal point is there in the measurement. So, it is counted as a significant figure.
Example: 600.00, there are 5 significant figures because the decimal point is given in the measurement.
In another case, if the decimal point is not there in the measurement. So the zero cannot be counted as a significant digit.
Example: 37, 000
This value is ambiguous, it is not clear whether it is measured exactly 37,000
Maybe it is measured to the nearest one, and got an exact number, got exactly 37,000, or maybe it is only measured to the nearest thousand. So, there is a little bit of ambiguity here. In this case, there is not complete information because the decimal point is not here. So, there are only 2 significant figures. ‘37’.
Here are also the example of zero: 2.5010-5 and 5.500 1012. The zeroes that are in bold faces are significant.
Rules of Significant Figures without a decimal point:
- On the FIRST non-zero digit, start counting for sig. figs.
- On the LAST non-zero digit, stop counting for sig. figs.
- Non-zero digits are always significant.
- Zeroes in between two non-zero digits are significant. All other zeros are insignificant.
Importance of Significant Figures:
- Significant figures are important to show the exactitude of the answer.using significant figures allow the scientist and engineers to know how accurate the answer is and how much changeability there is.
- Significant digits are important when using mathematics in certain fields so that you know how precise a measurement is. If you can only measure something to the nearest 10 meters or so you would write the number like 130 or 3540 but if you can go to the nearest meter you would go to 130. or 3540.Basically signaling how precise the measurement is. This is very necessary especially when doing lots of calculations So, you don’t take for granted that you have more or less precise measurements than you do and make errors or bad perceptions based on that.
Level of Accuracy:
Mathematicians or scientists who speak unlike languages agree on one common way of writing a measurement down and its having the level of accuracy behind that measurement that is easily understood by all. The foremost idea behind “significant figures” is to get everyone in the world. It is an accord that everyone says yes to use so that there is no confusion when one person reads another person’s work. There are a hundred different ways to represent accuracy in the measurement.but the above strategy is the simplest way to get the accuracy in the measurement.
How does our sig fig calculator work?
Our sig fig calculator works in two manners. It performs arithmetic operations on multiple numbers (for example 6.38 / 4.99) or simply rounds a number to the aspiration numbers or significant figures.Just enter the number that you desire to have formatted with significant figures and the calculator will display the result.
Modes Of Significant Figures:
We can calculate significant figures by hand or by using the sig fig calculator. For instance, we have the digits 0.003563 and want 2 significant figures. The trailing zeros are placeholders, so we do not count them. Next we round 3563 to 2 digits, leaving us with 0.0036.
Now we will consider an example that is not a decimal. Suppose we want 2,452,528 to 4 significant figures. We simply round the full number to the nearest thousand, giving us 2,453,000.
Significant Figures In Addition and Subtraction:
There are rules regarding the operations – Addition, Subtraction.
When performing the operation 14.12 + 3.42 – 0.45, the value with the least number of significant figures (2) is 0.45. Hence, the result must have two significant figures as well: 14.12 + 3.42 – 0.45 = 17.09 = 17.The result of an operation cannot have more significant figures that the value with the least number of significant figures.
Significant Figures In Multiplication and Division:
In this case, it is sufficient to do all calculations at once and apply the significant figures rules to the end of the result.If performing only division and multiplication.
Example: 16.12 * 2.10 / 4.6 = 12.852 / 4.6 = 2.793913 .
The round off value is 2.8
Here we do mixed calculation Addition, Subtraction, Multiplication and Division.
Example: 6.12 – 3.6 * 2.45 / 3.2 , After first step you will obtain 6.12 – 8.82 / 3.2 and in the second step you got 6.12 – 2.75625 and then 3.36375.
Now simply round the result leaving the last to significant figures.3.363 =3.4