Error Significant Figures Exact Numbers

What are Significant Figures?

Significant figures of a number are difits that takes useful contribution to the resolution of measurement  Dimensions are the technique of interconnecting with physical quantities in physics. A numeric value is yielded by each measurement. 

As a number given below, each digit is crucial for the measurement process. Consequently, a few digits are more significant than others. Now, let’s study some of these significant digits.

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What are Significant Digits?

The objective of significant figures for numbers is to take the meaning which contributes to its measurement resolution. 

  • The number 14.3 is included with three significant digits. All the time significant digits are known as the non-zero digits.

  • 6.14134 possess 6 significant digits. Here, all the numbers offer useful information. Also, 59 have two significant digits, and 78.3 have three significant digits.

  • 1000 has only one significant digit as the one is remarkable; we don’t recognize anything certainly about the units, tens, and hundreds of places, but the place holders are the zeroes in that number.

  • It is also the same with the number having a decimal given as 0.00028, which contains 2 significant digits i.e., only the 2 and 8 tell us something. The total availability of zeros is only the placeholders, and help to aid the information about approximate size.

  • Two thousand five (2005) has 4 significant digits i.e. the two and five are significant and we need to sum the zeroes as they’re between 2 the significant digits.


What are the Rules for Significant Figures?

The number of significant figures can be determined in a number by using these 3 rules:

  1. It the zeros are between two significant digits will also significant 

  2. In the decimal, a last zero or behind zeros share is significant only

  3. Non zero digits are always significant 


1. Rules for Addition and Subtraction Use are as Follows:

  • Add or subtract in the standard way

  • In the decimal, portion calculates the number of significant figures only of each number in the problem

  • To the right of the decimal, the final answer may have no extra significant figures than the MINIMUM number of significant figures in any number in the problem.


2. Rules for Multiplication and Division are as Follows:

  • The MINIMUM amount of significant figures in any number of the problem governs the number of significant figures in the answer. 

  • It implies that you have to distinguish significant figures to use this rule.


Significant Figures Errors in Measurements


1. Systematic Errors

This type of error arises from a fault in the measurement system, which frequently happens each time while a measurement is completed. 

You must elude the same thing by doing it wrong each time during the measurement, i.e., your calculation will fluctuate systematically (which means each time it is in the same direction) from the accurate outcome. 


2. Absolute and Relative Errors

If there is the uncertainty in the number and having similar units as the number itself, then it is known as the absolute error in a measured quantity. 

For illustration, if you distinguish a length is 0.658 m ± 0.003 m; then the absolute error is 0.003 m.

The relative error is also known as the fractional error. It is found by dividing the absolute error in the number by the number itself. This kind of error is ordinarily more significant than the absolute error.


3. Random Errors

This kind of error ascends from the variations that are most simply perceived by creating multiple trials of a specified measurement. 

For illustration, if you were to measure a pendulum’s period numerous times with the help of a stopwatch, you would discover that your measurements are not always identical.


What is the Correct Number of Significant Figures?

The correct number for the significant figures can be explained as significant numbers. It lies between 0 to 9 and is utilized as the coefficient of an expression clarifying the exactness of expression. 

Some of the following numbers are given in the table for illustrations with decimal notation, scientific notation as well as significant figures:


Decimal Notation

Scientific Notation

Significant Figures

1,234,000.00

1.234 * 106

4

123400000 * 106

9

0.00007650000

7.65 * 10-5

3

7650000*10-5

7

- 0.0000000100

-1 * 10-8

1

-1.00 * 10-8

3


What is Significant Figures Example?

Significant figures examples can be assimilated into a gradient of rules for significant figures;

  • Zeroes that lie between non-zero digits are significant: 2003 kg has 4 figures.

  • Entire non-zero digits are significant: 5.231g has four significant figures.

  • Following zeroes, which are also to the right of a decimal point in a number are significant: 0.0350 mL has three significant figures.

  • Foremost zeros to the left of the first non-zero digits are not significant.

  • When a number finishes in zeroes that are not to the right of a decimal point, the zeroes are not necessarily significant: 260 kilometers, maybe 2 or 3 significant figures.

FAQ (Frequently Asked Questions)

Q1. What is 18.5 Multiplied by 21.62, Taking into Account Significant Digits?

Ans: The calculator speaks that the product is 399.97.

Here, 18.5 have three significant digits, and 21.62 have four. So, we have to use three significant digits as our answer. That makes the answer 399.

Q2. What is the Sum of 9.8, 17, and 5.456, Taking into Account Significant Digits?

Ans: Here’s how you do the sum:

     9.8

+ 17

+   5.456

________

   32.256

Here as per the addition rule of significant figures, the answer will be 32.256, which has five significant figures.

Q3. Why is it Significant All the Time to Use the Precise Number of Significant Figures While Resolving a Problem?

Ans: Its significance in science and engineering is due to the lack of error, and also the measuring device can measure with 100% exactness.

The precise answer can be obtained through the significant figures. These are important to show the accurate answer. 

The application of the significant figures sanctions the experts to identify the precise answer.

Q4. What is the Reason Behind the Conversion Factors that Disturb the Number of Significant Figures in a Problem?

Ans: As per its true nature, the conversion factors do not sum for significant figures for they are precise values, and also they are not measurable quantities.