Converting Three Hundred Ninety-Eight and Two Thousandths into Decimal Form

Understanding how to convert a mixed number with specific decimal place values into its decimal form is a fundamental concept in mathematics. This guide will walk you through the process using the example three hundred ninety-eight and two thousandths.

Step-by-Step Breakdown

The given problem is to write three hundred ninety-eight and two thousandths in decimal form. This involves breaking down the number into its components and then placing it in the correct decimal position.

Breaking Down the Number

Whole Number Part: The term three hundred ninety-eight represents the whole number. This can be written as 398. Decimal Part: The term two thousandths indicates the position of the digit 2 in the thousandths place.

Combining the Parts

To combine the whole number and the decimal part, follow these steps:

Place the Whole Number: Write the whole number 398 as it is. This will occupy the spaces to the left of the decimal point. Place the Decimal Point: After the whole number 398, place a decimal point. Determine the Decimal Places: For two thousandths, place the digit 2 in the thousandths place, which is the 3rd position to the right of the decimal point.

Final Decimal Form

Therefore, three hundred ninety-eight and two thousandths written in decimal form is:

398.002

This means that 398.002 is the complete representation of the mixed number, where the whole number portion is 398 and the decimal part is 0.002.

Place Value Explanation

To further clarify, let's revisit the place value system:

The first decimal place (tenths) is represented by 0.1. The second decimal place (hundredths) is represented by 0.01. The third decimal place (thousandths) is represented by 0.001.

Thus, in the number 398.002:

398 represents the whole number part. 002 is placed in the thousandths place, indicating that the number has two thousandths.

Additional Examples

To solidify your understanding, consider these additional examples:

Four hundred and five thousandths: 400.005 Six hundred forty-two and seven thousandths: 642.007 Eight hundred and nine thousandths: 800.009

Conclusion

By following these steps and understanding the place value system, you can easily convert any mixed number into its decimal form. This knowledge is essential for various mathematical operations and real-world applications involving measurements and precise calculations.