Define Significant FiguresBack to Top
Significant figures are also known as significant digits.
The significant digits do not include zeros present in a number, as place holders or zeros appended to present a greater precision than that is actually present. Numbers with 100% reliability are known as Exact numbers, like the counted number of people or objects and the whole number conversion factors. An exact number is considered to have infinite number of significant digits.
Significant Figures RulesBack to Top
- All non zero digits are significant. For example, the number 82 has two significant digits and 4.35 has three significant figures.
- Zeros placed between non zero digits are significant. Each of the Numbers 9.02 and 803 have three significant digits.
- Zeros to the left of first non zero digit in a number are not significant. These zeros function only as place holders. For example, both the numbers 0.24 and 0015 have only two significant digits.
- Trailing zeros of a number with a decimal point are significant as the presence of these zeros indicate rounded measures. For example, the number 1.20 means that it is rounded to the hundredth and hence has three significant digits.
- The significance of trailing zeros in a number not containing a decimal point cannot be determined by mere observation. For example, The number 23,400 may be given precise to a unit or rounded to the nearest hundred. In the first case, the the number has three significant digits while the rounded number has 5 significant figures.
In the last case, different notations are used to indicate whether the trailing zero is significant or not.
- A bar is placed above the last significant digit or it is underlined.
- If all the trailing zeros are significant, a decimal point is placed after the last zero in the number.
- Writing the number in scientific notation clears the ambiguity.
Rounding Significant FiguresBack to Top
- Counting for significant digits is done from left to right. If the given number is a decimal less than 1.0, the counting of significant digits start from the first non zero digit.
- Round up. That is, add 1 to the last digit counted, if the immediate digit to its right is greater than or equal to 5 and not all the other digits following are zero. Round down (retain the number) if the digit to the right is less than 5.
- If the immediate digit to the right of number to be rounded is 5 followed by all zeros, the digit is rounded up to the next even number if odd, and the digit is retained if even.
- Ignore all the other digits. Append enough zeros to keep the number to the right size.
The following table demonstrates the rounding done on numbers to different significant numbers.
|| Rounded to
| Rounded to
| Rounded to
|7.0500|| 7|| 7.0|| 7.05|
In the last two case, the digit is rounded up or down to an even digit, if it is followed by 5 with trailing zeros.
7.0500 is rounded down to two significant digits as 7.0 as the digit rounded 0 is even. On the other hand, 8.13500 is rounded up to three significant digits as 8.14, as the digit rounded 3 is odd.
Adding Significant FiguresBack to Top
- The numbers are added just as two decimal numbers are added.
- Round the answer to the least number of decimal places in the decimal portion of any number.
The second number has 6 significant digits with three decimal place.
50.85 + 100.280 = 151.130 gms
The measure 50.85 has the least number of decimal places.
Hence, the sum of two measures = 151.13 gms.
Subtracting Significant FiguresBack to Top
The lesser number of decimal places 2 is observed in the measure 14.38 seconds.
Hence, the difference is rounded as 7.52 seconds.
Multiplying Significant FiguresBack to Top
The area which is the product of these two measures is to be rounded to two significant digits.
6.52 x 0.65 = 4.238 = 4.2 sq.ft when rounded to two significant digits.
Dividing Significant FiguresBack to Top
15.8 $\div$ 0.25 = 63.2 = 63
Significant Figures ProblemsBack to Top
Quantity of solvent released = 8.9 - 4.38 = 4.52
Out of the two reading, 8.9 ml has lesser number of decimal places which is one. Hence, rounding 4.38 to one decimal place.
The quantity of solvent released = 4.5 ml