Problem 143 - College Algebra Essentials

Question

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\left(4 \times 10^{3}\right)+\left(3 \times 10^{2}\right)=4.3 \times 10^{3}$$

Step-by-Step Solution

Answer

The provided statement is true.

Step 1: Understand the Statement

Observe the statement \(\left(4 \times 10^{3}\right)+\left(3 \times 10^{₂}\right)=4.3 \times 10^{3}\). This is the sum of two numbers in scientific notation. Remember, numbers in scientific notation are represented as \(a \times 10^{n}\), where \(a\) is between 1 and 10 and \(n\) is an integer.

Step 2: Evaluating the left-hand side of the equation

Simplify the left-hand side of the equation by converting the numbers from scientific notation to standard notation. \(4 \times 10^{3} = 4000\) and \(3 \times 10^{2} = 300\). Adding these numbers together gives \(4000 + 300 = 4300\).

Step 3: Evaluating the right-hand side of the equation

Simplify the right-hand side of the equation by converting the number from scientific notation to standard notation. \(4.3 \times 10^{3} = 4300\).

Step 4: Verify the Mathematical Statement

Compare the results derived from the left-hand side and right-hand side of the equation. If they are equal, the statement is true. Otherwise, if they are not equal, the statement is false. As both the left-hand side and right-hand side simplifies to 4300, the statement is indeed true.