Verified Answer :
- Identify the whole number: the word "three" represents \(3\).
- Recognize the decimal separator: "and" indicates the decimal point.
- Translate the fractional part: "seventy-nine thousandths" corresponds to the decimal \(\frac{79}{1000} = 0.079\).
- Combine the parts: Adding the whole and decimal parts gives the result, \(\boxed{3.079}\).
Explanation
- Analysis of the Number Components
The number is written as "three and seventy-nine thousandths". In decimal notation, the word "and" signifies the position of the decimal point. The phrase is divided into two distinct components: the whole number part and the decimal (fractional) part. The whole number part is "three," which is simply \(3\). The fractional part is "seventy-nine thousandths."
- Converting the Fractional Part
The term "seventy-nine thousandths" means the number 79 is placed such that its last digit ends in the thousandths place. The thousandths place is the third position to the right of the decimal point.
Writing this as a fraction:
\[\frac{79}{1000}\]
Converting this to decimal form:
\[\frac{79}{1000} = 0.079\]
To verify this, note that the digit 9 is in the third decimal place (thousandths), and the digit 7 is in the second decimal place (hundredths), while the first decimal place (tenths) is filled with a 0 as a placeholder.
- Final Assembly of the Number
Finally, combine the whole number part and the fractional part. By adding the components together, we get:
\[3 + 0.079 = 3.079\]
This results in the standard decimal form of the number provided.
Examples
Decimal notation is essential in everyday life, especially when dealing with measurements or financial transactions. For example, if you are purchasing materials for a construction project and need to cut a piece of wood that is "three and seventy-nine thousandths" of a meter long, representing it as \(3.079\) meters allows you to accurately measure the distance using a standard metric tape measure or tool calibrated in decimals. This precise notation ensures consistency and reduces errors in technical fields like engineering, science, and trade.