Sig Fig Calculator

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Significant figures calculator converts a given number into a new number with the desired amount of significant figures and solves expressions with sig figs. 
This tool can be used for your academic assignments as well as for professional fields where you get to do a lot of work with numbers. 

Significant figures definition

Sig figs are all the digits that are additional to the magnitude of a number. To avert repetitive figures that are not significant, you can round the given number.
However, you have to be very careful lest you end up losing precision while rounding. Most of the time, rounding numbers are meant for simplicity only. 

Sig Fig Rules

To determine which of the numbers are significant and which ones are not, you can use the rules of the Significant figure listed below:

...

The ‘0’ to the left of the decimal value less than 1 is not to be considered significant.

Leading zeros that occur before the first decimal number are not considered as significant figures.

For Example:

...

All of the trailing zeros that are place-holders, are not to be considered significant except when the decimal point is specified.

In many contexts, trailing zeros are only displayed if they are significant: for instance, if a gauging that is precise to four decimal places (0.0001) were to be given as 12.23, then it would usually be mistaken to show that just the two of decimal places of precision are available

...

Zeros that occur between non-zero digits are significant.

let's find out how many sig figs are in 1101

according to the rule "All non-zero numbers are considered as the significant numbers" there are 3 sig figs. numbers when we combine both rules then we will get the correct answer which is 4.

...

All non-zero number values are significant.

All non-zero number values are significant.
it is very simple rules that all numbers from 1-9 considered as a significant digit. 
for example: ( 011234567890 )
in the above example, there are 11 digits but have only 9 significant numbers.

How to round significant figures?

Rounding significant figures comes into play when you go for mixed calculations - addition/subtraction and multiplication/division - you need to round the value for each step of calculations to the correct number of significant figures. 

For instance, to calculate: 13.14+2.82×2.513.14 + 2.82 \times 2.5,

after first step you’d obtain the following result: 13.14+7.0513.14 + 7.05.

Then, you have to round the result of multiplication to 2 significant figures, obtaining 13.14+7.0513.14 + 7.05

Now, just add the numbers and leave two significant figures, attaining the result of 13.14+7.05=20.19=2013.14 + 7.05 = 20.19 = 20.

Rounding Rules

  • When rounding off numbers to a certain value of significant figures, do so to the closest value.
    Example 1: 
    Roundto3significantfigures:2.3578×102 \mathrm{Round to 3 significant figures:} 2.3578 \times 102
    Answer:2.36×104 \mathrm{Answer:} 2.36 \times 104
    Example:2: 
    Roundto2significantfigures:1.534×105 \mathrm{ Round to 2 significant figures:} 1.534 \times 105
    Answer:1.5×103 \mathrm{Answer:} 1.5 \times103
  • What to do if you encounter a 5?
    There is an arbitrary approach to that: If the figure before 5 is odd, round up. If the figure before 5 is even, then just let it be. The argument for this is that in the path of sequences of many calculations, any errors in rounding would be averaged out.

How to use the significant digits calculator

To work your way around with sig figs with our adding/multiplying significant figure calculator, just enter the number or the expression and the round to significant figure and that is it. 
Our sig figs calculator has two functions - it executes arithmetic operations on different numbers (for instance \(4.18 / 2.33\) or simply rounds a digit to the desired number of a significant figure.
 

References

  1. Wikipedia - Significant figures
  2. Chemistry in the Community; Kendall-Hunt: Dubuque, IA 1988
  3. Engelbrecht, Nancy; et al. (1990). "Rounding Decimal Numbers to a Designated Precision" (PDF). Washington, D.C.: U.S. Department of Education.

 

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David P. Felton | 06/08/2019

Loved this calculator. I am so impressed with this online Sig Fig calculator of yours.

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