What are Significant Figures?
Significant figures are any digits that add to the value of a number. Whole numbers, such as 11 or 21, have a definite value that is not expandable. However, there are indeterminate numbers, such as the value of Pi that have no end. For these indeterminate numbers, the unending series of numbers create the circle of a wedding ring or the sphere effect of a bubble. To use them properly in a calculation, there is a point where the added value is insignificant and is no longer considered crucial until, suddenly, with modern techniques where exact measurements become more crucial to success, the extension of significant figures beyond the traditional stop point becomes an essential part of the calculation.
Significant Figures Rules
To find more exact values, the realm of mathematics created rules to determine what makes up a significant figure. Those rules include:
- When there is only one number to the left of the decimal point and that number is zero, then the zero is not significant
- Place-holding zeros are not significant
- Any number of zeros that lie between nonzero numbers are significant
- All nonzero numbers are significant
- It is proper to round up or down when the number of significant numbers goes beyond the desired amount
- Significant numbers include zeros at the end of a number that are not removed because the removal would change the value
How to Use the Sig Fig Calculator
The significant figures calculator uses two modes to make its calculations. The sig fig is a good calculator to make traditional mathematical calculations such as multiplication and division of numbers, or it can be used as a tool to accurately round numbers to the desired significant figure designated by the operator.
Bear in mind that all hand-held calculators have a limited digital face on which to display significant numbers and are necessarily programmed to round at the limits of the space that digital numbers can occupy. As a result, most hand-held significant figures calculators will automatically round at 13 to 17 significant digits if the calculations demand that many digit places to reach accuracy.
These calculators can also accept instructions from the operator to limit the significant figures displayed. When an operator asks the significant figures calculator to define the first 21 significant figures of Pi, which is 3.14159265358979323846 to five digits, then the calculator automatically rounds the value of Pi to 3.1416. If the operator limits the significant figures to 11 numbers, then the calculator shows 3.1415926536 as the value of PI. For standard calculations, limiting Pi to five digits is acceptable. For work that is highly sensitive to finding an accurate number, many mathematicians utilize large (super) computers and request the use of outlandish significant figures.
Significant Figures in Operations
It is important to note that there are additional rules for using significant figures in operations such as addition, subtraction, multiplication, and division. Those rules include:
- The significant figure result of any operation cannot be more than the number of significate places used in any part of the calculation. For instance, a calculation that subtracted 2.46 from 12 leaves 9.54. Since the least number of significant figures used in the calculation is two, then the number is rounded to two significant digits or 9.5. Consider this as the significant figure result rule.
- When performing addition or subtraction only during a calculation, it is permitted to do all the calculations in sequence and then apply the significant figure result rule
- When performing multiplication and division only during a calculation, it is permitted to do all the calculations in sequence and then apply the significant figure result rule
- When performing addition and subtraction along with multiplication and division, it is required to round out each step per the significant result rule before applying the next sequence in the calculation
- Exact values such as whole numbers need not be considered significant figures and subject to the significant figure result rule. They are considered as having an infinite number of zeros
Using a significant figures calculator improves accuracy and limits costly mathematical errors. The rules are built into the significant figure calculator, so it is not necessary for you to stop and remember which rule applies when you are calculating.