Significant Figures Rules Addition Subtraction Multiplication Division Pdf
When dealing with numbers in science or mathematics, it is essential to understand the concept of significant figures. Significant figures, also known as significant digits, are the digits in a number that carry meaning and contribute to its accuracy. In this article, we will discuss the rules for addition, subtraction, multiplication, and division when dealing with significant figures.
What Are Significant Figures?
Significant figures are the digits in a number that give it accuracy and meaning. They are the digits that are not zero, and they start from the leftmost non-zero digit. For instance, in the number 0.0031, the significant figures are 3 and 1. The zeros are not significant because they are trailing zeros.
Significant figures are used to indicate the precision of a number. The more significant figures a number has, the more precise it is. It is essential to understand how to work with significant figures when performing mathematical operations to avoid losing precision in the result.
Rules for Addition and Subtraction
When adding or subtracting numbers with significant figures, the rule is to keep the same number of decimal places as the number with the fewest decimal places. For instance, if you are adding 2.45 and 3.6, the result would be 6.05, not 6.05. The number 2.45 has two decimal places, while 3.6 has one decimal place.
Let's consider another example. If you are subtracting 1.2345 from 6.789, the answer would be 5.55 as you only consider the decimal places present in the smallest number.
Rules for Multiplication and Division
When multiplying or dividing numbers with significant figures, the rule is to keep the same number of significant figures as the number with the fewest significant figures. For instance, if you are multiplying 4.32 and 2.5, the answer would be 11 instead of 10.8. The number 2.5 has only two significant figures, while 4.32 has three significant figures.
Let's consider another example. If you are dividing 8.3 by 1.2345, the answer would be 6.72 as you only consider the least number of significant figures that is present in the smallest amount of number.
Combining Addition, Subtraction, Multiplication, and Division
When combining addition, subtraction, multiplication, and division in a single equation, follow the order of operation. Parenthesis can help you determine the order of operation. Do the calculations inside the parenthesis before proceeding with other operations outside of the parenthesis.
Let's consider an example of combining addition, subtraction, multiplication, and division. Suppose you are solving for the following equation: (3.81 + 0.28) × 1.50 / 4.7. The first operation will be (3.81 + 0.28) which will be 4.09, then you will multiply it by 1.50, and the result is 6.135. The last operation is dividing it by 4.7, and the answer would be 1.3042, but we round it off to 1.30 as it only has two significant figures.
Conclusion
Significant figures are essential when dealing with scientific or mathematical calculations. It helps us determine the accuracy of our results. When adding or subtracting, we keep the decimal places the same as that of the least decimal places. When multiplying or dividing, we keep the same number of significant figures as that of the least number of significant figures. And, when combining addition, subtraction, multiplication, and division, we follow the order of operation to arrive at the correct result. Understanding these rules for significant figures is vital for any scientific or mathematical calculations, so make sure to practice these rules in your calculations.