Practice Problems: Significant Figures (Answer Key)
In Physics, measurement plays an important role. The smallest magnitude of a quantity that can be measured by an instrument is called least count of that instrument (For eg: the least count of metre scale is 0.1 cm). Since there is a least count associated with each instrument, the results of measurements made with it, always have limited accuracy. Let a quantity measured by an instrument be given by 87.2. The quantity is written up to the first decimal place. This indicates that the least count of the measuring instrument is 0.1. The digits 8 and 7 are reliable and certain while the last digit 2 in the given number (87.2) is uncertain by an amount ± 1. So, the given number has three significant figures. Thus, the significant figures are the number of digits required to report the result of an experiment or a calculation accurately. It is that number of digits in a quantity that is known reliably, plus one that is uncertain. As the number of significant figures increases, the accuracy also increases. For example, if the period of oscillation of a simple pendulum is measured as 1.45 seconds, the digits 1 and 4 are reliable and certain, while the digit 5 is uncertain. Thus, the measured value has three significant figures. Consider an iron rod whose length is measured as 5.6 cm using a metre scale. The value is observed as 5.61 cm when measured with a vernier caliper. In the first case, the length is measured with an accuracy of 1/10th of a centimetre while in the second case it is 1/100th of a centimetre. The number of significant figures is 2 with the metre scale while it is 3 that with the vernier calipers. Hence the most accurate value of the length is 5.61 cm with significant figures. If the same measured quantity is represented in other units, there is no change for the significant figures. i.e., 5.61 cm = 5.61 × 10-2 cm. Here also the number of significant figures is 3. Table of Contents
Rules for determining significant figuresThe rules for determining the number of significant figures are:
Below table gives you significant figures for different numbers. NumbersSignificant Figures2456424.56424.0540.245640.0245640.2456050.02456050.03520.00712456.052456.2066300263.0046.30046.32046.03240.0000603244.86 ×10534.860 × 10544.8 × 10-420.4 × 10-412.64 × 10253Table 1: Different numbers and their significant figures Rules for rounding significant figuresRounding off is made in correcting a physical quantity with least variation from its original value after dropping insignificant figures. The rules for rounding off numbers to the appropriate significant figures are given below:
For example, the number 8.26 rounded off to two significant figures is 8.3, while the number 8.24 would be 8.2. For any complex multi-step calculation, one digit more than the significant digits should retain in intermediate steps, and round off to proper significant figures at the end of the calculation. Also, learn the order of magnitude of a physical quantity. Rules for Arithmetic operations with Significant figuresWhen an experiment Is performed, a number of observations are made and the result is obtained by computing (adding, subtracting, multiplying, dividing) different data. The computed result cannot be more accurate than the original measurement which has the fewest significant figures. Rules for Multiplication and Division with significant figuresIn multiplication and division, the computed result should retain the significant digits, equal to those present in the least significant number involved in the calculation. Examples:
Rules for Addition and Subtraction with significant figuresIn addition or subtraction of given numbers, the same number of decimal places is retained in the result as are present in the number with the least number of decimal places. Examples:
Significant figures solved examples1. The result of an experimental calculation corrected up to seven significant figures is 7.363573. Round it off to six, five, four, three and two significant figures.
2. The length, breadth and thickness of a rectangular sheet of metal are 2.324m, 2.005m and 1.01 cm respectively. Find the surface area and volume of the sheet to the correct significant figures.
3. 6.84 g of a substance occupies 1.3cc. Express its density by keeping the significant figures in view.
4. The mass of a box measured by a grocer’s balance is 3.1 kg. Two gold piece of masses 22.35 g and 22.39 g are added to the box. What is (a) the total mass of the box, (b) the difference in the masses of the pieces to the correct significant figures?
5. The radius and length of thin wire are measured to be 0.54mm and 33.5 cm respectively. Find the volume of the wire up to the appropriate number of significant figures.
6. Each side of a cube is measured to be 8.405 m. Calculate the total surface area and the volume of the cube to appropriate significant figures.
The significant figures and their different rules are discussed in this article. What are 3 significant figures examples?For example, 20,499 to three signifcant figures is 20,500. We round up because the first figure we cut off is 9. 0.0020499 to three significant figures is 0.00205. We do not put any extra zeros in to the right after the decimal point.
How do you round to 3 significant figures?To round it off to 3 significant figures, we require to round it off to 6 decimal places after the decimal point. 0.0001366 = 0.000137 correct to 3 significant figures. (6) 7.304 → 7.30 correct to 3 significant figures. (7) 4.888 → 4.89 correct to 3 significant figures.
How many is 3 significant figures?Rounding to significant figures. |