Problem 55 - Algebra 1

Question

Use a calculator to evaluate the expression. Round your answer to two decimal places. $$8.3+y^{3} \text { when } y=-4.6$$

Step-by-Step Solution

Answer

The value of the given expression, after rounding to two decimal places, is -89.73.

Step 1: Calculate the cube of y

Plug the value of y into the expression and calculate the cube of y. So you have \((-4.6)^3\). Use a calculator to find the result.

Step 2: Sum with 8.3

Add the result from step 1 to the given number 8.3. Do the summation using a calculator.

Step 3: Round to two decimal places

Round the result from step 2 to two decimal places.

Key Concepts

Expression Evaluation

In mathematics, solving an algebraic expression involves substituting numbers in place of variables, and then simplifying the calculation step-by-step. The expression given in the exercise is an example of this process: \(8.3 + y^3\), where \(y = -4.6\). To evaluate this expression, you need to follow a sequence of straightforward actions:

• First, substitute \(y\) with \(-4.6\) in the expression. This follows the basic rules of algebra where each variable is replaced with a given value.
• Next, simplify the expression by calculating powers and performing addition. Here, the key operation is finding the cube of \(y\).

Using a calculator helps in accurately handling the computations, ensuring that each step delivers a precise result. Evaluating expressions is a fundamental skill in algebra; mastering it opens the gate to more complex algebraic problems.

Rounding Numbers

Once you arrive at a final number from the algebraic expression, the next task is to round it. Rounding is a method used to make a number simpler yet keeping it close to what it was. In the context of this exercise, we round the calculated result to two decimal places. Here's how it's typically done:

• Look at the third decimal place (just after your desired two decimal places). This digit determines how you round the number.


• If the third decimal is 5 or greater, increase the second decimal by 1. Otherwise, leave the second decimal unchanged.

Rounding is crucial because it provides a way to express a number with precision that's suitable for the context, such as making it easier to interpret and communicate especially in real-world applications and reports.

Cube of a Number

The cube of a number refers to multiplying the number by itself twice. Mathematically, it means \(y \times y \times y\) or \(y^3\). In the exercise, you encounter the task of cubing \(-4.6\). Calculating cubes is fundamental because it frequently appears across various fields of mathematics, physics, engineering, and computer algorithms. Important points to remember:

• When you cube a negative number, the result remains negative because multiplying three negative numbers still results in a negative product, given the laws of algebraic operations.


• Use a calculator to handle such computations for better accuracy, avoiding manual errors, especially with more complex or large numbers.

Understanding the concept of cubing helps with grasping more complicated functions and problem-solving techniques in algebra and beyond.