What is the expanded form of this number?
18.029
(1×10)+(8×1)+(2×1100)+(9×1100)
(1×10)+(8×1)+(2×110)+(9×1100)
(1×10)+(8×1)+(2×110)+(9×11,000)
(1×10)+(8×1)+(2×1100)+(9×11,000)
The Correct Answer and Explanation is:
The correct expanded form of the number 18.029 is:
(1×10) + (8×1) + (0×0.1) + (2×0.01) + (9×0.001)
Let’s break down the components of the number 18.029 step by step and explain how we derive the expanded form.
Step 1: Understanding the Place Value System
In the number 18.029, we have:
- 18 in the whole number part (before the decimal point).
- .029 in the decimal part (after the decimal point).
To expand the number, we must recognize the place value of each digit in both the whole number and decimal parts:
- 1 is in the tens place (value of 10).
- 8 is in the ones place (value of 1).
- 0 is in the tenths place (value of 0.1), but since it’s zero, it doesn’t contribute to the sum.
- 2 is in the hundredths place (value of 0.01).
- 9 is in the thousandths place (value of 0.001).
Step 2: Writing the Expanded Form
To write the expanded form of 18.029, you multiply each digit by its respective place value:
- The 1 is in the tens place, so its value is 1×10.
- The 8 is in the ones place, so its value is 8×1.
- The 0 is in the tenths place, but it has no contribution, so we omit it from the expanded form.
- The 2 is in the hundredths place, so its value is 2×0.01.
- The 9 is in the thousandths place, so its value is 9×0.001.
Thus, the expanded form of 18.029 is:
[
(1×10) + (8×1) + (0×0.1) + (2×0.01) + (9×0.001)
]
Step 3: Interpreting the Expanded Form
The expanded form represents the number as the sum of its individual place values. By writing it this way, we can better understand the contribution of each digit to the overall number. Here’s how it breaks down:
- 1×10 represents the ten’s place (10).
- 8×1 represents the one’s place (8).
- 2×0.01 represents the hundredths place (0.02).
- 9×0.001 represents the thousandths place (0.009).
Adding these together:
[
(1×10) + (8×1) + (2×0.01) + (9×0.001) = 10 + 8 + 0.02 + 0.009 = 18.029
]
Step 4: Conclusion
Therefore, the expanded form of 18.029 is correctly written as:
[
(1×10) + (8×1) + (0×0.1) + (2×0.01) + (9×0.001)
]
This explanation helps clarify how the number is broken down into its place values. Each digit contributes to the overall sum in the appropriate place value, allowing us to represent the number in an expanded form.