Mastering Significant Figure Calculations- A Guide to Multiplying and Dividing in Scientific Notation
How to Multiply and Divide Significant Figures with Scientific Notation
In scientific notation, numbers are represented in a concise form, which makes it easier to perform calculations involving very large or very small numbers. When multiplying or dividing numbers in scientific notation, it is crucial to maintain the correct number of significant figures to ensure the accuracy of the results. In this article, we will discuss how to multiply and divide significant figures with scientific notation, and provide some practical examples to illustrate the process.
Multiplying Significant Figures with Scientific Notation
To multiply significant figures with scientific notation, follow these steps:
1. Multiply the coefficients (the numbers before the “x10” part) of the two numbers in scientific notation.
2. Add the exponents (the numbers after the “x10” part) of the two numbers in scientific notation.
3. Write the product in scientific notation, using the coefficient from step 1 and the new exponent from step 2.
4. Determine the number of significant figures in the result by applying the “rounding rule” to the coefficient.
Example:
Let’s multiply the following numbers in scientific notation:
(3.45 x 10^3) x (2.1 x 10^2)
1. Multiply the coefficients: 3.45 x 2.1 = 7.305
2. Add the exponents: 10^3 x 10^2 = 10^(3+2) = 10^5
3. Write the product in scientific notation: 7.305 x 10^5
4. Apply the rounding rule: Since the last digit in the coefficient is 5, we round the coefficient to 7.3 (keeping only one significant figure).
Therefore, the final answer is: 7.3 x 10^5
Dividing Significant Figures with Scientific Notation
To divide significant figures with scientific notation, follow these steps:
1. Divide the coefficients (the numbers before the “x10” part) of the two numbers in scientific notation.
2. Subtract the exponents (the numbers after the “x10” part) of the two numbers in scientific notation.
3. Write the quotient in scientific notation, using the coefficient from step 1 and the new exponent from step 2.
4. Determine the number of significant figures in the result by applying the “rounding rule” to the coefficient.
Example:
Let’s divide the following numbers in scientific notation:
(1.23 x 10^4) ÷ (2.5 x 10^2)
1. Divide the coefficients: 1.23 ÷ 2.5 = 0.492
2. Subtract the exponents: 10^4 ÷ 10^2 = 10^(4-2) = 10^2
3. Write the quotient in scientific notation: 0.492 x 10^2
4. Apply the rounding rule: Since the last digit in the coefficient is 2, we round the coefficient to 0.49 (keeping two significant figures).
Therefore, the final answer is: 0.49 x 10^2
By following these steps, you can accurately multiply and divide significant figures with scientific notation, ensuring the integrity of your calculations.
