The weight og Darrin’s phone is 3.405 ounces. What is 3.405 written in expanded form?
A. 3×1+4×1/10+5×1/1,000
B.3×10+4×1/10+5×1×1/1,000
C.3×10+ 4× 1/10+5× 100
D.3× 1+4× 1/100+5× 1/1,000
The Correct Answer and Explanation is :
To express the number 3.405 in expanded form, we need to break it down into its individual place values. Each digit in a number represents a different value based on its position. The number 3.405 consists of the whole number part (3) and the decimal part (0.405).
Here’s the breakdown:
- Whole Number Part:
- The digit 3 is in the units place (1s place), which is equal to (3 \times 1) or simply (3).
- Decimal Part:
- The digit 4 is in the tenths place, which means it is (4 \times \frac{1}{10}) or (0.4).
- The digit 0 in the hundredths place has no value, so it does not contribute to the expanded form.
- The digit 5 is in the thousandths place, which means it is (5 \times \frac{1}{1000}) or (0.005).
Putting all these parts together, the expanded form of 3.405 is:
[
3 \times 1 + 4 \times \frac{1}{10} + 5 \times \frac{1}{1000}
]
Thus, the correct choice is A. (3 \times 1 + 4 \times \frac{1}{10} + 5 \times \frac{1}{1000}).
Explanation:
Expanded Form: This is a way to express a number by showing the value of each digit. In the case of 3.405, each digit’s contribution is highlighted by multiplying it by the value of its place. The whole number part represents the integer value, while the decimal part represents fractional values.
Significance of Each Choice:
- Choice A accurately represents the number using the correct place values.
- Choice B incorrectly uses (10) instead of (1) for the whole number part.
- Choice C uses (10) and (100) inappropriately for the decimal values.
- Choice D mislabels the tenths place as (1/100), which should actually be (1/10).
Understanding expanded form is crucial in mathematics as it lays the groundwork for further concepts such as addition, subtraction, and the understanding of decimals. It also helps clarify the contributions of each digit in a number, making calculations easier and more intuitive.