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Chapter 1: Problem 3

Simplify and round your answer to the correct number of significant figures. $$256.28-251.13$$

Short Answer

Expert verified
The final result after subtraction and rounding to the correct number of significant figures is 5.15

Step by step solution

01

Perform the Subtraction

Subtract 251.13 from 256.28. It gives a result of 5.15
02

Round to Correct Number of Significant Figures

Since both numbers in the subtraction operation have two figures after the decimal point, the answer should also have two figures after the decimal point. The rounded result is 5.15

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Key Concepts

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

Rounding
Rounding is an important skill in mathematics. It simplifies numbers to make them easier to work with. When rounding numbers, it's crucial to keep the context in mind to avoid losing essential information.

Here's how to round numbers properly:
  • Identify which digit needs rounding. This is often given or determined by the problem's context, such as the number of significant figures.
  • Look at the digit immediately to the right. If this digit is 5 or higher, you round up by adding one to the identified digit.
  • If this digit is 4 or lower, you keep the identified digit the same and drop all digits to the right.

It's helpful to understand the purpose behind rounding: it provides a manageable approximation. Aim to mirror the precision of your initial measurements when deciding on significant figures.
Subtraction
Subtraction is a basic arithmetic operation. It involves taking one number away from another and finding the difference. In the given problem:
\[256.28 - 251.13\]
We begin by aligning the numbers vertically, ensuring the decimal points are aligned. You then subtract as you would with whole numbers starting from the right and moving left.

To carry out subtraction effectively:
  • Always align decimal points to keep corresponding digits correctly aligned.
  • Subtract starting from the smallest place value to the largest.
  • If necessary, "borrow" from the next left digit to carry out the subtraction at each step.
Once you get the result, it's essential to check your work. Double-checking helps ensure the correct outcome, especially in academic settings.
Decimal Points
Decimal points are pivotal in ensuring precise calculations. They separate whole number parts from fractional parts. In any arithmetic operation involving decimals, aligning decimal points is crucial for accuracy.

When adding or subtracting numbers with decimals:
  • Write the numbers in a column form and make sure the decimal points are in a straight line.
  • Add zeros to numbers where necessary to ensure all numbers have the same amount of decimal places for easier calculation.
  • Perform the arithmetic with attention, checking to maintain the decimal point alignment.

This ensures accuracy in the result. Practice helps in gaining efficiency with decimal point operations, especially in settings where many arithmetic calculations are required.

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Most popular questions from this chapter

\(f(x)=5[[x]]-2\) (Hint: The greatest integer function is found under the option INT in a graphing calculator.)

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