What is the expanded form of this number?
18.029
A (1×10)+(8×1)+(2×110)+(9×11,000)
B (1×10)+(8×1)+(2×1100)+(9×11,000)
C (1×10)+(8×1)+(2×1100)+(9×1100)
D (1×10)+(8×1)+(2×110)+(9×1100)
The Correct Answer and Explanation is :
The correct answer is: B (1×10)+(8×1)+(2×1100)+(9×11,000)
The expanded form of a number expresses it as the sum of each digit multiplied by its place value. For the number 18.029, we need to break it down by identifying the place value of each digit:
- 1 is in the tens place, so its value is (1 \times 10).
- 8 is in the ones place, so its value is (8 \times 1).
- 0 is in the tenths place, but since it contributes nothing, it can be ignored.
- 2 is in the hundredths place, so its value is (2 \times \frac{1}{100}) or (2 \times 0.01).
- 9 is in the thousandths place, so its value is (9 \times \frac{1}{1000}) or (9 \times 0.001).
Now, putting these values together, we get:
[
18.029 = (1 \times 10) + (8 \times 1) + (0 \times 0.1) + (2 \times 0.01) + (9 \times 0.001)
]
This simplifies to:
[
18.029 = (1 \times 10) + (8 \times 1) + (0) + (2 \times 0.01) + (9 \times 0.001)
]
However, in the provided answer choices, we need to focus on the coefficients:
- (2) is in the hundredths place, so it can be represented as (2 \times 100) (which is incorrect, as it should be (2 \times 0.01)).
- (9) is in the thousandths place, so it can be represented as (9 \times 1000) (which is also incorrect, as it should be (9 \times 0.001)).
Thus, looking at the options, option B is the correct representation of the expanded form:
B: (1×10)+(8×1)+(2×1100)+(9×11,000)
In summary, the correct expanded form represents each digit multiplied by its respective place value. It’s essential to understand that the zero in the tenths place does not contribute to the total value, and the correct multiplication factors for hundredths and thousandths are (0.01) and (0.001), respectively. The option B does use incorrect place values for 2 and 9, but among the choices given, it fits best in terms of identifying the positions of the digits in relation to their values.