Significant Figures - Definition, Rules, FAQs

Edited By Team Careers360 | Updated on Jul 02, 2025 04:56 PM IST

Define significant figures

Significant number is also known by some other names like significant digits, precision or resolution. Whereas significant meaning in English is important or noticeable.

What are significant figures?

The number that is provided in the form of digits is established using significant figures. These digits represent numbers in a meaningful way. Instead of figures, the term significant digits is frequently used. By counting all the values starting with the first non-zero digit on the left are considered as significant numbers and from this we may determine the number of significant digits.

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Definition of significant figures

Significant numbers or figures can be defined as the particular number or the digits which are able to express the meaning of the number based on its accuracy. The number 6.658, for example, includes four significant digits. These significant figures give the numbers more clarity. Significant digits is another name for them.

Significant figures examples can be considered as 13.57 in this it will include four significant digits and in case of 0.00751 then it has 3 significant figures. These all calculation of significant figure is generally based upon some rules which can be defined as follows:

Significant figures rules

There are some rules on the basis of which we can count the significant digits these rule can be explained in the manner described below:

1. All non-zero numbers are of significant nature. This can be explained by taking an example of 123456789 that contains exactly 9 significant digits.

2. Every zero which occurs between any two non-zero digits is also considered a significant number; this can be explained by taking the example of 107.0093 in which seven significant numbers are present.

In both cases counting of figures can be easily done by just counting the digits present like in the first example 123456789 digits present are nine which corresponds to 9 significant figures and in the case of 107.0093 seven digits are present which corresponds to seven significant figures.

3. Rule number three states that every zero which is present on the right hand side of a decimal point and also left to the non-zero digit is said to be non-significant in nature. This can be explained by taking the example of 0.00583 this represents only three significant figures are there as zeroes are present on left hand side which are considered as non-significant digits whereas 583 which are non-zero digits are said to be of significant nature thus 0.00583 contains only 3 significant figures.

4. This rule states zeroes which are present on the right hand side of a decimal point are said to be significant whereas a non-zero digit is not able to follow this rule. Example where this rule can be applied is 20.00 which contains four significant figures whereas if zeroes are present at the left side like 0.002 then it contains only one significant figure.

5. Rule number five states that zeroes which are on the right hand side towards zero to last digit number of decimal points are considered as significant digits whereas those which are present at left side are considered as non-significant. For example 0.0087900 in this number 5 significant digits are present whereas the zeroes in the left hand side before non-zero digit are considered as non-significant figures.

6. The last rule for finding out significant numbers considers that all the zeros which are present on the right hand side of the last non-zero digit are said to be significant if they will be found from the measurement value. For example 1234 m is considered to have 4 significant figures.

Hence these are rules by which we can easily calculate the number of significant figures present in any number whereas figures mean the presence of a number of digits in any value. It is also to be said that a natural number can contain an infinite number of significant figures like if we talk about a bag which contains 5 balls then it can also be written as 5.000000……. balls in a bag this specify that any natural number can contain an infinite number of significant figures.

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Rounding off of significant figures:

By leaving one or more digits from the right, a number is rounded off to the required number of significant digits. The last digit kept should remain constant when the initial digit in the left is less than 5. The last digit is rounded up when the first digit is greater than 5. The number kept is rounded up or down to get an even number when the digit left is exactly 5. When there are multiple digits remaining, rounding off should be done as a whole rather than one digit at a time.

Rounding off any digits has rules too. These rules can be explained as the following manner:

1. At first we must determine to which digit the rounding off should be applied. If the number after the rounding off digit is less than 5 then all the numbers on the right side must be eliminated. This can be explained by taking the example of 1.24003 then rounding off will be 1.24.

2. However, if the digit next to the rounding off digit is more than 5, we must add 1 to the rounding off digit and ignore the remaining numbers on the right side. This rule is also considered as (n+1) rule. This can be explained by taking the example of 1.2478 to three figures then it is written as 1.25.

One of the main questions is often asked: why are significant figures important? This can be explained on the basis of the importance of significant figures that enable us to keep track of measurement quality. Significant figures basically show how much to round while also ensuring that the result is not more precise than our beginning number. In short we can say that it gives us a more accurate result.

Significant numbers are also an important term in maths where a significant digit can be defined as the number of digits in a value or we can say which is used frequently in a measurement of any value which contributes the most exact or we can say most precise value is known as significant figures. We start to count significant figures from the very first non-zero digit present.

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NCERT Chemistry Notes:

Frequently Asked Questions (FAQs)

1. How many significant figures are present in 1.2678?

All the digits present here are non-zero so by counting all the digits present here we can calculate the significant figures and here are five significant figures present.

2. How to find significant figures in 0.0017?

In this case we will consider the rule of significant figures which states that zeroes present on the left hand side will not be considered as significant one so in this only 2 significant figures are there which are non-zero i.e. 1 and 7.

3. How can we say that there are an infinite number of significant numbers in a single value?

A natural number can contain an infinite number of significant figures like if we talk about a bag which contains 5 balls then it can also be written as 5.000000……. balls in a bag that specify that any natural number can contain an infinite number of significant figures.

4. Significant figure in 127.09?

Significant figures present in 127.09 is five as all digits will be considered as significant one.

5. Round off to 3 digits to 1.26781

Here the digit next to the rounding off digit is more than 5 then we must add 1 to the rounding off digit and ignore the remaining numbers on the right side thus the value will be 1.27.

6. What are significant figures in chemistry?

Significant figures, often called "sig figs," are all the digits in a measured value that are known with certainty, plus one digit that is estimated or uncertain. They indicate the precision of a measurement and are crucial in scientific calculations and reporting results accurately.

7. Why are significant figures important in chemistry?

Significant figures are important because they convey the precision of a measurement or calculation. They help prevent overstating the accuracy of results, ensure consistency in scientific communication, and maintain the integrity of data throughout complex calculations.

8. How do you determine which digits are significant in a number?

To determine significant figures, follow these rules: 1) All non-zero digits are significant. 2) Zeros between non-zero digits are significant. 3) Leading zeros are not significant. 4) Trailing zeros after a decimal point are significant. 5) Trailing zeros in a whole number are significant only if there's a decimal point.

9. How do significant figures affect calculations?

In calculations, the result should have no more significant figures than the least precise measurement used. This ensures that the calculated result doesn't imply greater precision than the original data supports.

10. What is the "round to the first uncertain digit" rule?

This rule states that when reporting a calculated result, you should round to the first digit that's uncertain. This digit is typically the rightmost significant figure in the least precise measurement used in the calculation.

11. What's the difference between accuracy and precision in relation to significant figures?

Accuracy refers to how close a measurement is to the true value, while precision relates to the reproducibility of measurements and is indicated by significant figures. A measurement can be precise (have many significant figures) but not accurate, or accurate but not precise.

12. What is the concept of "limiting reactant" in relation to significant figures?

The limiting reactant in a chemical reaction determines the maximum amount of product that can be formed. In calculations involving limiting reactants, the number of significant figures in the final answer is determined by the reactant measurement with the fewest significant figures.

13. How do you handle addition and subtraction with significant figures?

In addition and subtraction, the result should have the same number of decimal places as the least precise measurement (the one with the fewest decimal places). This ensures that the uncertainty in the result matches the least precise input.

14. How do significant figures apply to multiplication and division?

In multiplication and division, the result should have the same number of significant figures as the measurement with the fewest significant figures. This rule helps maintain the appropriate level of precision in the calculated result.

15. How do you deal with significant figures in multi-step calculations?

In multi-step calculations, it's best to carry all digits through intermediate steps and round only the final answer. This prevents rounding errors from accumulating and ensures the final result has the appropriate number of significant figures.

16. What are guard digits and when should they be used?

Guard digits are extra digits carried through calculations to prevent rounding errors. They're typically one or two digits beyond the number of significant figures needed in the final answer and are rounded off at the end of the calculation.

17. What's the relationship between significant figures and standard deviation?

Standard deviation, which measures the spread of data, is typically reported with one or two significant figures. The number of significant figures in the standard deviation often guides how many to use in reporting the mean of the data set.

18. How do you handle significant figures in graphing and curve fitting?

When graphing data or performing curve fitting, use all available digits to create the graph or fit the curve. However, when reporting parameters derived from the fit, use the appropriate number of significant figures based on the precision of the original data.

19. How do you apply significant figures rules to numbers in scientific literature?

When using numbers from scientific literature, assume all reported digits are significant unless stated otherwise. If uncertainty is provided (e.g., 1.23 ± 0.01), use this to determine the appropriate number of significant figures in calculations.

20. How do you apply significant figures rules to numbers obtained from computer calculations?

Computer calculations often produce results with many digits. It's important to round these results to the appropriate number of significant figures based on the precision of the input data, rather than reporting all digits generated by the computer.

21. How do you handle zeros in significant figures?

Zeros can be tricky in significant figures. Leading zeros are never significant (e.g., 0.00123 has 3 sig figs). Captive zeros (between non-zero digits) are always significant (e.g., 1005 has 4 sig figs). Trailing zeros after a decimal are significant (e.g., 1.200 has 4 sig figs).

22. What's the difference between exact numbers and measured numbers in terms of significant figures?

Exact numbers (like counting numbers or defined quantities) have infinite significant figures, while measured numbers have a limited number of significant figures based on the precision of the measurement.

23. How do you write numbers in scientific notation while preserving significant figures?

In scientific notation, move the decimal point so that only one non-zero digit is to its left. Then, express the number as that digit (and any following significant digits) times 10 to an appropriate power. For example, 0.00304 (3 sig figs) becomes 3.04 × 10^-3.

24. What's the difference between rounding and truncating in significant figures?

Rounding involves adjusting a number to the nearest desired significant figure, while truncating simply cuts off digits beyond the desired point. Rounding is generally preferred as it provides a more accurate representation of the original number.

25. How do you express very large or very small numbers with significant figures?

Use scientific notation to express very large or small numbers while preserving significant figures. For example, 0.000000304 (3 sig figs) becomes 3.04 × 10^-7, and 1,540,000,000 (3 sig figs) becomes 1.54 × 10^9.

26. What role do significant figures play in error analysis?

Significant figures help in expressing the uncertainty in measurements and calculations. They provide a quick way to estimate the magnitude of potential errors and ensure that reported results don't imply more precision than is justified by the data.

27. How do you handle significant figures in logarithms?

For logarithms, the number of decimal places in the result should equal the number of significant figures in the original number. For example, log(1.23 × 10^5) = 5.09, where 1.23 × 10^5 has 3 significant figures, so the result has 3 decimal places.

28. What's the relationship between significant figures and instrumental precision?

The number of significant figures in a measurement should reflect the precision of the measuring instrument. For example, if a balance measures to 0.01 g, a mass of 10.54 g would be reported with 4 significant figures.

29. How do significant figures relate to the concept of uncertainty in measurements?

Significant figures implicitly express the uncertainty in a measurement. The last significant figure represents the digit with some uncertainty, while all preceding digits are considered certain within the limits of the measuring device.

30. What's the difference between precision and significant figures?

Precision refers to the reproducibility of measurements, while significant figures are a way of expressing that precision numerically. More significant figures generally indicate higher precision, but they don't necessarily imply accuracy.

31. How do you handle significant figures in exponential expressions?

In exponential expressions like e^x or 10^x, the number of significant figures in the result is determined by the number of significant figures in the exponent. For example, e^(2.4) would have two significant figures in the result.

32. What's the role of significant figures in dimensional analysis?

In dimensional analysis (unit conversion), the number of significant figures in the final answer should match the measurement with the fewest significant figures used in the calculation, regardless of the number of conversion factors used.

33. How do you determine significant figures in measured values with units?

The units don't affect the number of significant figures. Focus on the numerical value and apply the standard rules for identifying significant figures. For example, 1.20 km has three significant figures, just as 1.20 does.

34. What's the importance of significant figures in reporting experimental results?

Significant figures in experimental results convey the precision of the measurements and the reliability of the data. They prevent overstating the accuracy of results and allow other scientists to assess the quality of the data.

35. How do you handle significant figures with constants like π or e?

Mathematical constants like π or e are considered to have infinite significant figures. In calculations, use at least one more digit of these constants than the number of significant figures in your least precise measurement.

36. How do you apply significant figures rules to percentages?

Percentages follow the same rules as other measurements. For example, 98.3% has three significant figures, while 98% has two. Be cautious with percentages like 100%, which could have 1, 2, or 3 significant figures depending on the context.

37. What's the concept of "implied uncertainty" in relation to significant figures?

Implied uncertainty refers to the understood margin of error in the last significant figure of a measurement. For example, a measurement of 1.23 g implies an uncertainty of ±0.01 g in the last digit.

38. What's the difference between "significant digits" and "significant figures"?

The terms "significant digits" and "significant figures" are often used interchangeably. Both refer to the digits in a number that carry meaningful information about the precision of the measurement.

39. How do you determine significant figures in numbers written in scientific notation?

In scientific notation, count all non-zero digits and zeros between them. For example, 3.0040 × 10^5 has five significant figures. The power of 10 does not affect the number of significant figures.

40. What's the importance of significant figures in stoichiometry calculations?

In stoichiometry, significant figures ensure that calculated quantities of reactants or products don't imply more precision than the given data allows. The least precise measurement in the problem determines the precision of the final answer.

41. How do you handle significant figures when converting between different units?

When converting units, the number of significant figures in the result should match the number in the original measurement, regardless of the conversion factor used. This preserves the original precision of the measurement.

42. What's the role of significant figures in analytical chemistry?

In analytical chemistry, significant figures are crucial for accurately reporting concentrations, masses, and volumes. They help in expressing the precision of analytical instruments and the reliability of quantitative analysis results.

43. How do you apply significant figures rules to very small numbers close to zero?

For very small numbers, leading zeros are not significant. For example, 0.00304 has three significant figures. Using scientific notation (3.04 × 10^-3) can help clarify the number of significant figures in such cases.

44. What's the concept of "surplus precision" in relation to significant figures?

Surplus precision occurs when more digits are reported than are justified by the measurement's precision. This can lead to misinterpretation of data accuracy and should be avoided by adhering to significant figure rules.

45. How do you handle significant figures in equilibrium constant calculations?

In equilibrium constant calculations, carry extra digits through intermediate steps and round the final K value to the number of significant figures determined by the least precise concentration measurement used in the calculation.

46. What's the relationship between significant figures and the precision of measuring instruments?

The precision of measuring instruments determines the number of significant figures that can be reported. For instance, a balance that measures to 0.01 g allows reporting of two decimal places, typically resulting in three or four significant figures for most measurements.

47. What's the importance of significant figures in pH calculations?

In pH calculations, the number of decimal places in the pH value corresponds to the number of significant figures in the hydrogen ion concentration. For example, a pH of 4.7 implies two significant figures in [H+].

48. How do you handle significant figures in rate constant calculations in kinetics?

In kinetics, rate constants should be reported with the same number of significant figures as the least precise measurement used in the calculation. This ensures that the reported rate constant doesn't imply more precision than the experimental data supports.

49. What's the role of significant figures in spectroscopy measurements?

In spectroscopy, significant figures are crucial for reporting wavelengths, frequencies, and intensities. They reflect the precision of the spectrometer and help in accurately identifying and characterizing spectral features.

50. How do you apply significant figures rules to numbers obtained from logarithmic scales?

For numbers obtained from logarithmic scales (like pH or decibels), the number of decimal places indicates the number of significant figures. For example, a pH of 5.67 has three significant figures.

51. What's the concept of "precision creep" in relation to significant figures?

Precision creep occurs when calculations or data processing inadvertently introduce extra digits, implying greater precision than the original measurements justify. Adhering to significant figure rules helps prevent this issue.

52. How do you handle significant figures in thermodynamic calculations?

In thermodynamic calculations involving quantities like enthalpy or entropy, carry all digits through intermediate steps and round the final result to the number of significant figures determined by the least precise measurement used in the calculation.

53. What's the importance of significant figures in reporting molar masses?

Molar masses should be reported with an appropriate number of significant figures based on the precision of the atomic masses used. Typically, three to five significant figures are sufficient for most chemical calculations.

54. What's the role of significant figures in expressing confidence intervals?

When reporting confidence intervals, the number of significant figures should reflect the precision of the measurement and the size of the interval. Typically, the interval is reported with one or two significant figures, which then determines the precision of the central value.

55. How do you handle significant figures when dealing with very large numbers in astrophysical chemistry?

In astrophysical chemistry, where very large numbers are common, use scientific notation to express values while preserving appropriate significant figures. This approach maintains the precision of the measurement without writing out long strings of zeros.