Write five hundred and twenty-four thousandths as a decimal. 0.0524
The correct answer and explanation is:
Correct Answer: 0.524
To write five hundred and twenty-four thousandths as a decimal, first understand the meaning of the number in words. The word “thousandths” indicates that the number should be placed in the thousandths place, which is three digits after the decimal point.
Step-by-step breakdown:
- “Five hundred and twenty-four” means the number 524.
- “Thousandths” means this number is being divided by 1,000.
- So, 524 thousandths is equal to:
5241000\frac{524}{1000}
When this fraction is converted to a decimal, it becomes 0.524.
Place Value Analysis:
In the decimal 0.524:
- The digit 5 is in the tenths place (1st after decimal)
- The digit 2 is in the hundredths place (2nd after decimal)
- The digit 4 is in the thousandths place (3rd after decimal)
This confirms that the number represents 524 parts out of 1,000, or five hundred and twenty-four thousandths.
Common Mistake:
A common mistake is to confuse “five hundred and twenty-four thousandths” with “fifty-two and four thousandths,” which would be written as 52.004. Another mistake is to count the digits wrong and write 0.0524, which is fifty-two and four tenths of a thousand, or 52.4 thousandths, not 524 thousandths.
Understanding how place values work after the decimal point is essential. The first digit to the right of the decimal is tenths, then hundredths, then thousandths. Correct placement of digits based on the name of the number is critical for proper decimal representation.
Therefore, the correct decimal for five hundred and twenty-four thousandths is 0.524.