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Significant figures are also called significant digits, as they are established in the form of digits. The number of significant digits can be identified by counting all the values starting from the 1st non-zero digit located on the left. These numbers are reliable and necessary to indicate the quantity of a length, volume, mass, measurement, and so on. Arithmetic operations such as addition, subtraction, multiplication, and division are used while calculating significant figures.
|1.||What are Significant Figures?|
|2.||Rules of Significant Figures|
|3.||Rounding Significant Figures|
|4.||Solved Examples on Significant Figures|
|6.||FAQs on Significant Figures|
What are Significant Figures?
Significant Figures refer to the number of important single digits from 0 to 9 in the coefficient of the expression that conveys the message accurately. These significant figures help engineers or scientists in asserting the quantity of any measurement, length, volume, or mass. For example, 453 has three significant figures.
The two main applications to understand significant figures are - Precision and Accuracy. Let's learn how these two terms play an important role in real-life situations when it comes to the concept of significant figures.
Precision - The closeness between two or more quantities to each other under the same condition is called precision. In precision, the level of measurement when repeated gives the same result and the individual measurement agrees to each other.
Accuracy - The closeness between the measurement and the accurate number is called accuracy. Accuracy helps in providing consistent results with no error along with accuracy in the result.
Rules of Significant Figures
To measure the significant figures of a calculated measurement, there are certain rules that need to be followed and remembered.
- All the digits except zero are always significant. For example, 894621 contains six significant digits.
- Any zeros placed in between any two non-zero digits are significant. For example, 10.007 contains five significant digits.
- If zeros are placed both on the right of a decimal point and left of a non-zero digit, they are not significant. For example, 0.0012 contained two significant digits.
- If zeros are placed on the right of the decimal and not have a non-zero digit after that, then it is significant. For example, 80.00 contains four significant digits.
- Zeros placed on the right of the last non-zero digit after the decimal point are significant. For example, 0.00153100 contains six significant digits.
- Zeros that are placed on the right of the last non-zero digit are significant when they come from a measurement. For example, 3560 m contains four significant digits.
In the figure given below, there are 4 significant digits in the number 0.00003400
Rounding Significant Figures
Rounding significant figures is done by considering the first non-zero digit if we are rounding off up to one significant figure. Look at the next digit to the right, if it equals to or greater than 5, then add 1 to the first non-zero digit, if it is less than 5 deduct 1 from the first non-zero digit.
Rounding Significant numbers have two main rules:
- Identify the digit to be rounded off. If after rounding off the number, the number is less than 5 then all the numbers present on the right side needs to be excluded.
- Once the rounded-off digit is greater than 5 then the number 1 needs to be added to the rounding-off digit and exclude the other numbers on the right side.
For example, 0.05491 if we have to round this number to a three-digit significant figure, first check the last digit. In this case, the last digit is 1 which is lesser than 5, so it won't round up since these numbers are after the decimal point. Hence, the number will round up to 0.0549. Further round it to two-digit, it will be 0.055 since 9 is greater than 5 and is dropped to make the number 4 into 5.
Topics Related to Significant Figures
Check out these interesting articles to know more significant figures and its related articles.
Solved Examples on Significant Figures
Example 1: Write down the significant figures of the list of numbers 367, 0.0075, 56.004, 98.70, and 230.00
Solution: From the list of numbers, let us find out the significant figures of each number.
367 - Three significant figures
0.0075 - Two significant figures
56.004 - Five significant figures
98.70 - Four significant figures
230.00 - Five significant figures
Example 2: Find the significant figures from the sum of these numbers 67 + 12.6 + 3.40 + 22
Solution: First, we need to add the list of numbers to find the total sum.
67 + 12.6 + 3.40 + 22 = 105
Therefore, the significant digits are three which are 1, 0, and 5.
Example 3: Round off the list of numbers 34.05, 21.3, 76.9, 44.7 to two significant figures.
Solution: Keeping the rounding off rules in mind, let us round off every number one by one.
34.05 ~ 34
21.3 ~ 21
76.9 ~ 77
44.7 ~ 45
Practice Questions on Significant Figures
FAQs on Significant Figures
What are Significant Figures?
Significant Figures refer to the number of important single digits from 0 to 9 in the coefficient of the expression that conveys the message accurately. These significant figures help engineers or scientists in asserting the quantity of any measurement, length, volume, or mass.
Why do we Need Significant Figures?
Significant figures are the main aspects of statistics and mathematics that deal with accuracy and precision. They also help in showing how precise the end value is. Significant figures can be used in day-to-day life as well by anyone to find out the accurate figure.
What is Rounding Off Numbers?
Rounding numbers make a number simpler but keep the number close to its value. The rounded-off number may be less accurate but it is relatively close. People round out numbers in many situations that they face in their day-to-day life.
How does Accuracy Relate to Significant Figures?
The closeness between the measurement and the accurate number is called accuracy. Accuracy helps in providing consistent results with no error along with accuracy in the result. One of the main aspects of significant figures is the number being as accurate to the value or measurement itself.
When do Zeros be Considered Significant?
Zeros that are present between two non-zero digits in the number are considered significant. The zero can be present either on the left and right side of the decimal point. For example - 230.056 here zero is considered as significant and therefore, the significant numbers are six. All the trailing zeros after the decimal point are significant while all the trailing zeros in a whole number are non-significant.
When can the Value be Rounded off to get Significant Figures?
When the first digit of the rounded-off digit can be removed or when it is higher than the number 5, that is when the value can have significant figures.