Textbook Question
How many significant figures are there in each of the following values? (d) 0.07 x 10^8
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Ch 01: Concepts of Motion
Chapter 1, Problem 1
Perform the following calculations with the correct number of significant figures. (b) 5.1125 + 0.67 + 3.2
Verified step by step guidance1
Identify the number of decimal places in each number. Here, 5.1125 has 4 decimal places, 0.67 has 2 decimal places, and 3.2 has 1 decimal place.
When adding numbers, the result should have as many decimal places as the number with the least decimal places. In this case, it is 3.2 with 1 decimal place.
Add the numbers together without initially worrying about the significant figures: 5.1125 + 0.67 + 3.2.
Round the result of the addition to 1 decimal place, as determined in step 2.
Ensure that the final answer is expressed with the correct number of significant figures, which is determined by the least number of decimal places in the original numbers.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Significant Figures
Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. When performing calculations, the result should be reported with the same number of significant figures as the measurement with the least number of significant figures.
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Counting Significant Figures
Addition of Numbers with Significant Figures
When adding numbers, the result should be rounded to the least precise decimal place of any number in the operation. This means that the final answer should reflect the smallest number of decimal places present in the numbers being added. For example, if one number has two decimal places and another has one, the result should be rounded to one decimal place.
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Order of Operations
The order of operations is a set of rules that dictates the sequence in which calculations should be performed to ensure consistent results. In the context of addition, it is straightforward as all terms are added together, but understanding this concept is crucial when dealing with more complex calculations involving multiple operations, where parentheses and the order of operations can affect the outcome.
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Related Practice
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As an architect, you are designing a new house. A window has a height between 140 cm and 150 cm and a width between 74 cm and 70 cm. What are the smallest and largest areas that the window could be?
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Perform the following calculations with the correct number of significant figures. (a) 159.31 x 204.6
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