Problem 19 - Algebra 1

Question

Perform any indicated operation. Round the result to the nearest tenth and then to the nearest hundredth. $$ -25.349(-1.369) $$

Step-by-Step Solution

Answer

The product of -25.349 and -1.369 rounded to the nearest tenth is 34.7 and rounded to the nearest hundredth is 34.72.

Step 1: Muliplication

Multiply the absolute values of the two numbers: \( |25.349|\times |1.369| \). It gives you a product of 34.727281

Step 2: Check the signs

Since both numbers are negative, the product of two negative numbers is a positive number. So the product is \( +34.727281 \).

Step 3: Round to the nearest tenth

To round decimal number to the nearest tenth, look at the number in hundredths place. It is less than 5, so round down to 34.7.

Step 4: Round to the nearest hundredth

To round to the nearest hundredth, look at the number in the thousandths place. The number in the thousandths place is 2 which is less than 5, so keep the number in hundredths place as it is. So the rounded number is 34.72

Key Concepts

Rounding Numbers

Rounding numbers helps simplify complex decimal values, making them easier to use and convey. Let's start by understanding different places in a decimal number. When rounding, you focus on digits after the decimal point: tenths, hundredths, thousandths, etc. Knowing these places helps determine exactly how to round.

• To round to the nearest tenth, look at the digit in the hundredths place.
• If this digit is 5 or more, increase the tenths digit by 1.
• If it is less than 5, leave the tenths digit as it is.

For example, in the number 34.72, when rounding to the nearest tenth, look at the hundredths place: 2. It's less than 5, so you leave the tenths digit as it is, resulting in 34.7.
When rounding to the nearest hundredth, focus on the thousandths place, applying a similar rule. If the number is less than 5, keep it as it is; otherwise, round up. Rounding is a key skill in handling accuracy and precision in mathematics, especially when precise values complicate calculations or interpretations.

Negative Number Properties

In mathematics, understanding the properties of negative numbers is crucial for efficient problem-solving. Negative numbers are numbers below zero on the number line, having unique multiplication rules. Here's what to remember about them:

• The product of two negative numbers is positive. For instance, even though -25.349 and -1.369 are both negative, their product will be positive.
• The product of a positive number and a negative number is negative.

Grasping these properties lets you determine the signs of resulting products without confusion. Recognizing how negative numbers behave under multiplication helps manage calculations effectively, allowing for accurate mathematical operations.

Product of Numbers

When you multiply numbers, you're finding the 'product'. This operation is not limited to whole numbers but can be applied to decimals as well. Multiplication with decimals requires a focused approach, as precision is needed:

• First, consider the decimal places in each number separately.
• Multiply them as if they were whole numbers, ignoring the decimal points temporarily.
• After finding the raw product, count the total number of decimal places from both original numbers.
• Place the decimal point in the product accordingly.

For example, the numbers 25.349 and 1.369 both have three decimal places combined, therefore the decimal in their product, 34.727281, is appropriately situated.
Noting the number of decimals ensures accuracy, which is vital in mathematics. Understanding multiplication of decimals is an asset for tackling both theoretical and practical problems, making product computations much more manageable.