Significant figures or “sig figs” refer to all of the numbers which contribute to the meaning of a specific number’s overall value. To avoid repeating figures which aren’t significant, you have to round off the numbers. Practice caution when rounding so you don’t lose precision. Often, rounding numbers is only for the purpose of simplicity. To help you with any issues, you can use the sig fig calculator.
How to use the sig fig calculator?
When it comes to calculating significant figures, a lot of people get confused easily. This is why a significant figures calculator is extremely useful. With this calculator, you only have to input the required values and it does the work for you.
The significant digits calculator may seem confusing too, but once you start using it, you’ll discover how simple it is. Here are the steps to follow when using this calculator:
- First, enter the Number or the Expression.
- Next, there is an optional value for you to enter which is the Round to Sig Fig. You only have to enter this value if, on the first step, you entered the Number. But if you entered the Expression, you don’t have to input anything value here.
- After the first two steps, the rounding significant figures calculator will automatically generate several values for you. These include the Results, Significant Figures, and Steps #1, #2, and #3.
What does Sig Fig mean?
Now that you know how to use the sig fig calculator, let’s move to the significant figures for you to understand them better. In science and math, you often hear the term “significant figures,” “sig fig” or “significant digits.” These refer to the digits of a given number which contribute to the indication of how precise that number is.
In other words, the significant figures of a given number are the digits which have meaning that contributes to the resolution of its measurement. This includes all numbers except for:
- all of the leading zeroes;
- any trailing zeroes used as placeholders to imply the scale of a number;
- any introduced spurious digits, for instance, by any calculations performed to greater accuracy than that of the original data or the reported measurements to greater accuracy than supported by the equipment.
Significance arithmetic refers to the estimated rules which roughly maintain the significance throughout a specific computation. On the other hand, the propagation of uncertainty refers to the scientific rules which are more sophisticated.
The main reason why we round numbers is to prevent the reporting of insignificant figures. For instance, it may create an inaccurate precision to express a measurement such as 12.345000 kg, a number which contains 7 significant figures. If the scale you used only measures to the nearest gram, it will give you a measurement of 12.345 which only has 5 significant figures.
In some cases, people only round off numbers for the purpose of simplicity instead of doing this to indicate any precision of measurement. For instance, news writers round off numbers to make them easier and faster to state in their news broadcasts. When you’re trying to determine significant numbers from the non-significant ones, follow these rules:
- All zeroes to the left of a decimal value which are less than 1 aren’t significant.
- All of the trailing zeroes which serve as placeholders aren’t significant.
- The significant digits are all the zeroes between non-zero digits.
- All non-zero numbers are also significant.
If a number contains more significant digits than what’s needed, you may round off that number. For instance, if you have the number 432,500 and you only need 3 significant figures, then you can round it off to 433,000.
In some cases, zeroes found at the end of any given number aren’t significant but aren’t removed either. The reason for this is that removing these non-significant numbers may have an effect on the number’s value. Using the same example, you can’t remove the 3 zeroes unless you’re changing the number into scientific notation.
How do you round to 3 significant figures?
When it comes to significant figures, using any kind of sig fig calculators such as a multiplying significant figures calculator or a rounding significant figures calculator makes your job a lot easier. But if you want to perform all of the calculations manually, then you should know the basic rules for rounding numeric values:
- The digit that’s considered “most significant” is the one on the leftmost position. This doesn’t count any leading zeroes which only serve as placeholders and will never be significant figures.
- If you round off to a specific number of significant figures, the one that’s considered the least significant is the one farthest from the most significant figure. In such a case, the least significant figure can be zero.
- The very first non-significant figure is the n+1th figure.
Other rules for rounding off numbers include:
- If the first non-significant figure is lower than 5, this doesn’t change the least significant figure.
- If the first non-significant figure is higher than 5, you should increment the least significant figure by 1.
- If the first non-significant figure is 5, then you can either retain or increment the least significant figure.
- Remove all non-significant figures when rounding off numbers.
The technique of rounding off to a significant digit is very common. This is because you can apply it to any number no matter how small or how big it is.
For instance, when you read a report in the newspaper about a lottery winner who won $5 million, the writers have already rounded this figure to one significant digit. They have rounded it to the most significant figure in the whole number. Here are the steps to follow when rounding numbers t 3 significant figures:
- Look at the 2nd digit after the first significant figure.
- Draw a line after the place value of the required digit then check the next digit.
- Apply the rules for rounding off numbers.
- Then fill all of the spaces to the right of the vertical line with zeroes and only stop is there’s a decimal point.