Meaning of Significant Figures, Rules and Examples

When measuring something, you must use a certain measuring instrument. The measurement results in the form of numbers consist of numbers that match the measurement facts.

The result of a measurement can also be referred to as a ‘significant figure’. Now to better understand it, here is a complete explanation of what significant figures are and the rules for writing them.

Meaning of Significant Figures

The definition of significant figures is a series of numbers obtained from the measurement results of a measuring instrument consisting of exact figures and estimated figures.

Exact numbers themselves have the meaning of numbers that can be seen and read directly when using measuring instruments, while the meaning of estimated numbers is the last numbers that were estimated and cannot be seen or read using the same measuring instrument.

The estimated figure is also the number of accuracy obtained from the measuring instrument used, usually half of the measuring instrument.

The function of significant figures is to create a parameter that is agreed upon by all parties in a common way of making measurements with a certain level of accuracy. This method allows the measurement process to have a high level of accuracy as needed,

One example of the application of significant figures in real life can be seen in the industrial sector in science and engineering to show the accuracy of the correct measurement answer.

This method allows science scientists to make uncertainty measurements better than ever before.

Significant Figures Rule

When we want to write down significant figures, there are rules in physics that you must fulfill, among the rules for writing significant figures you can see through the points below.

  1. Significant figures consist of all digits, from 1 to 9 and are not zeros. For example, 717, the number 717 has 3 significant figures.
  2. Zeros must be written after non-zero digits are not considered significant figures. For example, the number 24,000, then the significant digits are only 2 and 4
  3. Zeros that are between two non-zero numbers are considered significant figures, for example, 509,000, so the significant digits are 5, 0 and 9.
  4. Zeros that are in front of a non-zero number are not considered significant figures. For example, 0.87, then the significant digits are only 8 and 7.
  5. Zeros written after the decimal sign and in front of them are non-zero numbers, then they are significant figures. For example 35,900, the significant digits are 3, 5, 9 and 0.

Example of Calculation of Significant Figures

There are several ways to count significant figures, to make it easier to understand, you can use the following methods:

Addition and Subtraction Rules

This method is used when a number is omitted from a number, the value of the last stored number will be determined in the rounding process. There is a rule when you use this method, first, numbers that are more than five and above will be rounded off, while numbers less than five must be eliminated.

Second, if it is exactly at number five, it will be rounded up according to the previous number. If the previous number is odd, then the number must be rounded up, but if the number is even then it must be removed.

  • Example Questions for Adding Significant Figures

a. For example, there is a number 34.89, then this number according to the addition method will be rounded up to 34.9. The same thing if there is a number 516.89 then it is rounded to 516.9. The same is done with other significant figures.

b. 223.210 kg → 0 is the estimated number.
73.4 kg → 4 is the estimated figure.
———– +
296.610 kg → The correct writing of the result is 296.6 kg.
c. 62.2 km → 2 is the estimated figure.
22,153 km → 3 is the estimated number.
——— –
84,353 km → The correct writing of the subtraction result is 84.3 kg.

Multiplication and Division Rules

The next way is multiplication and division, the rule in using this method is that you have to follow the number of numbers that is least at the end. If you do multiplication or division with significant figures with exact numbers, then the results follow the results of significant figures.

  • Example of Multiplication of Significant Numbers

a. For example, there is the number 34.231 kg multiplied by 0.25. You are asked to find the result using significant figures. When multiplied, it turns out that the answer is 8.5577, in order to convert it to a significant figure, the result of the multiplication is written with a significant figure of 8.56 kg.

b. 3.23800 g → 6 significant figures
2000 g → 3 significant figures
——– x
6476 g
Since there are at least 3 significant figures, the product must have 3 significant figures. The correct spelling is 6470 g.
c. 0.3325 kg → 4 significant figures
0.29 m3 → 2 significant figures
——— :
1.1465 kg/m3→ Writing the correct division result is 1.15 kg/m3

Rules for Calculation of Roots

The result of the root of a significant number, the rule may only use significant figures of the number of significant figures that are rooted.

  • Example of Rooting Significant Figures

A. 1234 = 35.12 0 → 4 significant figures.

B. 64 = 8 → 1 significant figure.

Rules for Calculation of Powers

For significant figures with exponents, the rule may only use significant figures with significant figures raised to the power of the power.

  • Example of Power of Significant Figures

A. (4.2 cm)3 = 74,088 cm3 → 74 cm3 (2 significant figures)

B. (3.25 kg)2 = 34.328125 kg2 → 34.4 kg2 (3 significant figures)

Rounding Rules

The last is the operation of rounding significant figures, the rule is that if the result of the operation is obtained, it can only use one approximate number, not more. If more, then the result will not be valid.

  • Example of Operation Questions for Rounding Significant Figures

Rounding off significant figures is also not much different from the previous two examples. For example, there is a number 2.45 cm in the square root of 3, when it is calculated the result is 14.706 cubic cm. Rounding is done by removing the number after the decimal, the result is 14.7 cubic cm.

The same thing is also done for taking roots, if there is a zero behind the decimal number, it will not be counted. For example, 2.70, the result of the significant digit is only 2.7 without any zeros.

That’s a brief explanation of significant figures that we can review, hopefully this information can help you, especially those who are having trouble calculating significant figures. You can read follow-up books on the same topic to make it easier to understand.

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