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Chapter 5: Problem 81

For Exercises \(71-82,\) simplify by using the order of operations. $$2.2-\left[9.34+(1.2)^{2}\right]$$

Short Answer

Expert verified
-8.58

Step by step solution

01

Evaluate the exponent

First, calculate \(1.2^{2}\). \(1.2^{2} = 1.44\).
02

Simplify inside the brackets

Next, add \(9.34\) and \(1.44\) together, because they're inside the brackets. \(9.34 + 1.44 = 10.78\).
03

Subtract from the remaining term

Lastly, subtract \(10.78\) from \(2.2\). \(2.2 - 10.78 = -8.58\).

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Key Concepts

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

Exponents
Understanding exponents is crucial in simplifying mathematical expressions.
Exponents tell us how many times we need to multiply a number by itself. For example, in the expression \(1.2^{2}\), the exponent 2 means that we multiply 1.2 by itself. Thus, \(1.2^{2} = 1.2 \times 1.2 = 1.44\).
Breaking it down:
  • Identify the base and the exponent.
  • Multiply the base by itself as many times as indicated by the exponent.
  • Proceed to the next step in the order of operations.

This step is vital because getting the exponent wrong will affect the entire calculation.
Brackets
Using brackets correctly helps organize the operations within a mathematical expression.
Brackets indicate that the operations inside them should be performed first. For example, in the expression \[2.2 - (9.34 + (1.2)^{2})\], we first need to evaluate the expression inside the inner brackets, (1.2)^{2}, and then add the resulting value to 9.34.
Steps to simplify:
  • Evaluate any operations inside the innermost brackets first.
  • Continue to solve any other operations within the outer brackets.
  • Finally, perform any remaining operations outside the brackets.

Correct use of brackets ensures each operation is calculated in the proper order, which is essential for accuracy.
Subtraction
Subtraction is one of the fundamental operations in arithmetic. It involves taking one number away from another.
In the expression \[2.2 - (9.34 + 1.44)\], once we have calculated the value inside the brackets, we subtract it from 2.2. The solution to this specific problem is \[2.2 - 10.78 = -8.58\].
Critical steps for performing subtraction:
  • Align the numbers by their decimal points if they are not already aligned.
  • Subtract starting from the rightmost digit to the leftmost.
  • If necessary, borrow from the next column if the top digit is smaller than the bottom digit.

Understanding subtraction will help you to accurately solve various mathematical expressions.

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Most popular questions from this chapter

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Perform the indicated operations. Round the answer to the nearest hundredth when necessary. $$\left(\frac{2}{7}\right)(5.1)\left(\frac{1}{10}\right)$$
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