Problem 14 - Fundamentals of Mathematics

Question

Use a calculator to find each value. \((0.006) \cdot(-0.241) .\) Round to three decimal places.

Step-by-Step Solution

Answer

The value is -0.001.

Step 1: Set Up the Multiplication

First, identify the numbers you need to multiply: the values given are 0.006 and -0.241.

Step 2: Perform the Multiplication

Use your calculator to multiply 0.006 by -0.241. Enter the calculation to get the product.

Step 3: Record the Result

After calculating, you will get the product of the multiplication, which is -0.001446.

Step 4: Round the Result to Three Decimal Places

Look at the product -0.001446. To round to three decimal places, consider the fourth decimal place, which is a 4. Since this number is less than 5, you round down, keeping the result as -0.001.

Key Concepts

Rounding Decimals

Rounding decimals is an essential skill for simplifying numbers, particularly in multiplication problems. When you have a result like -0.001446, rounding helps make the number easier to interpret. To round to three decimal places, you look at the number in the fourth decimal place. This is because the fourth digit assists in deciding whether the third digit should stay the same or increase by one.

• If the fourth digit is 5 or greater, you round up the third decimal place.
• If the fourth digit is less than 5, as in our example with the number 4, you round down, or rather keep the third place the same.

In our case, -0.001446 comes down to -0.001 after rounding. Understanding how to round correctly ensures the accuracy of your results, especially when precise decimal places are required.

Calculator Use

Using a calculator effectively can significantly improve your ability to handle decimal multiplications, especially when dealing with many decimal places or negative numbers. Here's a straightforward guide to using your calculator for decimal multiplication: - Enter each number in sequence. If you're multiplying 0.006 and -0.241, ensure you enter the negative sign correctly for the latter. - Use the multiplication function (usually labeled with an '*' or 'x'). - Complete the calculation by pressing 'equals', and your calculator will display the product. Calculators help minimize errors associated with manual multiplication, making them a valuable tool for precision math work. Additionally, using a calculator for more complex problems allows you to perform multiple calculations quickly, verifying outcomes and ensuring accuracy.

Negative Numbers Multiplication

Multiplying negative numbers, particularly decimals, involves a few rules that help simplify the process. With negative numbers, knowing the outcome without performing the multiplication can be insightful: - The product of two numbers with different signs (one positive, one negative) is always negative. - The absolute values are multiplied just like positive numbers would be. In our example, multiplying 0.006 by -0.241, you can expect a negative result due to the differing signs. Using rules of the sign helps maintain clarity about the direction (positive or negative) of the product. Understanding these rules gives you an edge in quickly anticipating results and mitigating errors tied to sign miscalculations.