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Chapter 1: Problem 4

Simplify and round your answer to the correct number of significant figures. $$586.1-580.12$$

Short Answer

Expert verified
The simplified and rounded off answer is 6.0.

Step by step solution

01

Perform the subtraction

First, subtract 580.12 from 586.1, which can be done using standard arithmetic calculation. This gives \(586.1 - 580.12 = 5.98\)
02

Determine correct number of significant figures

The rule states that for addition and subtraction, the final answer should retain the same number of decimal places as the measurement with the fewest decimal places. Thus the answer should have two decimal places as the number with the fewest decimal places, 586.1, has one decimal place.
03

Round off your answer

So we round off 5.98 to one decimal place, resulting in 6.0.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Subtraction
Subtraction is one of the fundamental operations in arithmetic, where you take away one quantity from another. In terms of notation, subtraction is often represented by the minus symbol (-). For example, in the given exercise, you subtract 580.12 from 586.1. The process involves aligning the numbers by their decimal points and subtracting each place value column starting from the right.
  • First, ensure that the numbers are lined up correctly, especially if they have different numbers of decimal places.
  • Start subtracting from the smallest place value, moving to the left.
  • Borrow from the column to the left if the top number is smaller than the bottom number in any column.
In our specific example, 586.1 - 580.12 gives us 5.98, which requires careful placement during each subtraction step. Understanding this basic operation is crucial for performing accurate arithmetic calculations.
Mastering Arithmetic Calculations
Arithmetic calculations encompass the four basic mathematical operations: addition, subtraction, multiplication, and division. In any arithmetic calculation, such as subtracting 586.1 by 580.12, accuracy is key.
  • Maintain precision by aligning decimal points to ensure all digits are in their correct place value positions.
  • Double-check calculations to avoid simple errors that can easily occur in manual subtraction.
  • Use a calculator for verification, especially with more complex numbers or when the result needs high precision.
For subtraction, keeping an organized approach with decimal alignment helps ensure the result is correct before moving on to rounding or other subsequent steps.
Rounding and Significant Figures
Rounding is the process of adjusting a number to be simpler or to conform to a specified number of significant figures. The concept of significant figures is critical in scientific and mathematical calculations, as it reflects the precision of measurements.
  • When rounding as part of subtraction, look at the first digit after your designated significant figure.
  • If this digit is 5 or greater, round up the last significant figure; if it's less than 5, keep the last significant figure as it is.
  • In the given exercise, the subtraction result 5.98 is rounded to one decimal place to comply with the original number 586.1, which has one decimal place, yielding a rounded answer of 6.0.
Understanding how to appropriately round to the correct number of significant figures ensures the final result accurately reflects the precision of the input numbers.

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