To write the number 5416789 in expanded form, we will break it down according to the place values of each digit. Here’s the step-by-step solution:
### Step 1: Identify the place values
The number 5416789 has the following digits:
- 5 in the ten lakhs place
- 4 in the lakhs place
- 1 in the ten thousands place
- 6 in the thousands place
- 7 in the hundreds place
- 8 in the tens place
- 9 in the ones place
### Step 2: Write each digit with its place value
Now, we will express each digit multiplied by its respective place value:
- The digit 5 is in the ten lakhs place: \(5 \times 10,00,000\)
- The digit 4 is in the lakhs place: \(4 \times 1,00,000\)
- The digit 1 is in the ten thousands place: \(1 \times 10,000\)
- The digit 6 is in the thousands place: \(6 \times 1,000\)
- The digit 7 is in the hundreds place: \(7 \times 100\)
- The digit 8 is in the tens place: \(8 \times 10\)
- The digit 9 is in the ones place: \(9 \times 1\)
### Step 3: Combine the expressions
Now we can combine these expressions to write the expanded form:
\[
5 \times 10,00,000 + 4 \times 1,00,000 + 1 \times 10,000 + 6 \times 1,000 + 7 \times 100 + 8 \times 10 + 9 \times 1
\]
### Step 4: Simplify the expression
Next, we can simplify this expression by calculating the values:
- \(5 \times 10,00,000 = 50,00,000\)
- \(4 \times 1,00,000 = 4,00,000\)
- \(1 \times 10,000 = 10,000\)
- \(6 \times 1,000 = 6,000\)
- \(7 \times 100 = 700\)
- \(8 \times 10 = 80\)
- \(9 \times 1 = 9\)
So, we can write the expanded form as:
\[
50,00,000 + 4,00,000 + 10,000 + 6,000 + 700 + 80 + 9
\]
### Final Answer
Thus, the expanded form of the number 5416789 is:
\[
50,00,000 + 4,00,000 + 10,000 + 6,000 + 700 + 80 + 9
\]
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