Question

Solve the following. Carry division to the hundredths place where necessary. \(472.4 \times 0.002=\) ______

Short answer

The answer is 0.94.

Step-by-step solution

Understand the Problem

We need to multiply the number 472.4 by 0.002 and give an answer up to the hundredths place.

Set Up the Multiplication

Write the numbers for multiplication: 472.4 and 0.002. Here, we are multiplying a whole number with a decimal.

Convert to Whole Numbers

Turn 472.4 into 4724 by removing the decimal point. Similarly, turn 0.002 into 2 by removing the decimal. We account for the decimal places after multiplication to adjust the final answer.

Multiply the Whole Numbers

Multiply 4724 by 2, which results in 9448.

Adjust for Decimal Places

Since the original numbers had a total of four decimal places (one from 472.4 and three from 0.002), place the decimal point in the product to match this, making it 0.9448.

Round to the Hundredths Place

Round 0.9448 to the nearest hundredth by looking at the thousandths place. Since the digit is 4, round down to 0.94.

Key concepts

Decimal Places

Decimal places refer to the digits that appear after a decimal point in a number. They are essential when dealing with fractions expressed in a decimal form. Understanding decimal places helps in accurately performing calculations and representing numbers. For example, in the number 472.4, there's one decimal place, and in 0.002, there are three decimal places.

When multiplying decimal numbers, the total number of decimal places in the result is the sum of the decimal places in the factors. This means that if one number has two decimal places and another has three, the product should have five decimal places. In calculations, it's crucial to be mindful of these placements since they affect the precision and interpretation of the result.

Rounding Numbers

Rounding numbers makes complex numbers easier to work with while maintaining a reasonable accuracy. It's a process of adjusting numbers to a specified degree of precision, usually to the nearest ten, hundred, or an important place like the nearest hundredth.

When rounding to a certain decimal place, it's necessary to look at the digit immediately after that position. For instance, to round 0.9448 to the nearest hundredth, examine the thousandths place (4 in this case). If this number is 5 or above, round up by increasing the hundredth place by one. Otherwise, the digits remain unchanged. Hence, 0.9448 becomes 0.94 because we round the thousandth place down.

• Decide which decimal place you need to keep.
• Check the next digit to decide if you round up or down.
• Adjust accordingly.

Step-by-Step Math Solutions

Step-by-step math solutions are crucial for learning and understanding how to approach and solve mathematical problems incrementally. Breaking down complex problems into smaller, manageable steps allows learners to follow a logical progression and keep track of each part of the process.

For example, solving the multiplication of 472.4 by 0.002 can be approached step-by-step as follows:

• Understand the problem: Determine what the question is asking.
• Set up the problem: Arrange the numbers for multiplication.
• Convert to whole numbers: Remove the decimals to simplify the multiplication.
• Multiply: Perform the multiplication of whole numbers.
• Adjust for decimal places: Reintroduce the decimal in the product to reflect initial decimal points.
• Round if necessary: Complete the solution by rounding to the required decimal place.

This systematic approach ensures accuracy and clarity, helping students both understand and replicate the process independently.