Write forty-one thousand, two hundred eleven in the place-value chart. Then write the number in expanded form.
The correct answer and explanation is:
Sure! Let’s break down the number forty-one thousand, two hundred eleven step by step.
Step 1: Write the number in digits
Forty-one thousand, two hundred eleven is written as:
41,211
Step 2: Place-value chart
Let’s write this number in a place-value chart. The place values from left to right are:
| Ten-Thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|
| 4 | 1 | 2 | 1 | 1 |
So, 41,211 is:
- 4 in the ten-thousands place (40,000)
- 1 in the thousands place (1,000)
- 2 in the hundreds place (200)
- 1 in the tens place (10)
- 1 in the ones place (1)
Step 3: Write the number in expanded form
The expanded form shows the value of each digit based on its place value, added together: 41,211=(4×10,000)+(1×1,000)+(2×100)+(1×10)+(1×1)41,211 = (4 \times 10,000) + (1 \times 1,000) + (2 \times 100) + (1 \times 10) + (1 \times 1)
or 41,211=40,000+1,000+200+10+141,211 = 40,000 + 1,000 + 200 + 10 + 1
Explanation (300 words)
Understanding place value is essential in reading, writing, and interpreting numbers correctly. In the number forty-one thousand, two hundred eleven, each digit has a specific place value that determines its contribution to the overall number.
The place-value chart helps us visualize this. Starting from the right:
- The ones place represents units or single ones.
- The tens place represents groups of ten.
- The hundreds place represents groups of one hundred.
- The thousands place represents groups of one thousand.
- The ten-thousands place represents groups of ten thousand.
So, the digit 4 in the ten-thousands place means we have four groups of ten thousand, which equals 40,000.
The digit 1 in the thousands place means one group of one thousand, or 1,000.
The digit 2 in the hundreds place means two groups of one hundred, or 200.
The digit 1 in the tens place means one group of ten, or 10.
Finally, the digit 1 in the ones place means one unit, or simply 1.
By adding all these values together, we reconstruct the number 41,211.
Writing numbers in expanded form helps build a strong understanding of how numbers are structured. It also aids in performing arithmetic operations like addition, subtraction, multiplication, and division. Understanding place value allows us to see the size or magnitude of each digit’s contribution to the whole number.
This is especially important in math learning and everyday life, such as reading prices, measuring distances, or understanding statistics.