Write each of the following numbers in expanded form :
(i) `15,768`
(ii) `3,08,927`
(iii) `24,05,609`
(iv) `5,36,18,493`
(v) `6,06,06,006`
(vi) `9,10,10,510`

Answer

To write the given numbers in expanded form, we will break each number down according to the place value of each digit. Here’s the step-by-step solution for each part of the question:

### (i) 15,768
1. Identify the place value of each digit:
- 1 is in the thousands place (10,000)
- 5 is in the hundreds place (5,000)
- 7 is in the tens place (70)
- 6 is in the units place (6)
- 8 is in the ones place (8)

2. Write the expanded form:
\[ 15,768 = 1 \times 10,000 + 5 \times 1,000 + 7 \times 100 + 6 \times 10 + 8 \times 1 \]

### (ii) 3,08,927
1. Identify the place value of each digit:
- 3 is in the lakhs place (3,00,000)
- 0 is in the ten thousands place (0)
- 8 is in the thousands place (8,000)
- 9 is in the hundreds place (900)
- 2 is in the tens place (20)
- 7 is in the ones place (7)

2. Write the expanded form:
\[ 3,08,927 = 3 \times 1,00,000 + 0 \times 10,000 + 8 \times 1,000 + 9 \times 100 + 2 \times 10 + 7 \times 1 \]

### (iii) 24,05,609
1. Identify the place value of each digit:
- 2 is in the ten lakhs place (20,00,000)
- 4 is in the lakhs place (4,00,000)
- 0 is in the ten thousands place (0)
- 5 is in the thousands place (5,000)
- 6 is in the hundreds place (600)
- 0 is in the tens place (0)
- 9 is in the ones place (9)

2. Write the expanded form:
\[ 24,05,609 = 2 \times 20,00,000 + 4 \times 1,00,000 + 0 \times 10,000 + 5 \times 1,000 + 6 \times 100 + 0 \times 10 + 9 \times 1 \]

### (iv) 5,36,18,493
1. Identify the place value of each digit:
- 5 is in the crores place (5,00,00,000)
- 3 is in the ten lakhs place (30,00,000)
- 6 is in the lakhs place (6,00,000)
- 1 is in the ten thousands place (10,000)
- 8 is in the thousands place (8,000)
- 4 is in the hundreds place (400)
- 9 is in the ones place (9)

2. Write the expanded form:
\[ 5,36,18,493 = 5 \times 5,00,00,000 + 3 \times 30,00,000 + 6 \times 6,00,000 + 1 \times 10,000 + 8 \times 1,000 + 4 \times 100 + 9 \times 1 \]

### (v) 6,06,06,006
1. Identify the place value of each digit:
- 6 is in the crores place (6,00,00,000)
- 0 is in the ten lakhs place (0)
- 6 is in the lakhs place (6,00,000)
- 0 is in the ten thousands place (0)
- 6 is in the thousands place (6,000)
- 0 is in the hundreds place (0)
- 0 is in the tens place (0)
- 6 is in the ones place (6)

2. Write the expanded form:
\[ 6,06,06,006 = 6 \times 6,00,00,000 + 0 \times 10,00,000 + 6 \times 6,00,000 + 0 \times 10,000 + 6 \times 1,000 + 0 \times 100 + 0 \times 10 + 6 \times 1 \]

### (vi) 9,10,10,510
1. Identify the place value of each digit:
- 9 is in the crores place (9,00,00,000)
- 1 is in the ten lakhs place (10,00,000)
- 0 is in the lakhs place (0)
- 1 is in the ten thousands place (10,000)
- 0 is in the thousands place (0)
- 5 is in the hundreds place (500)
- 1 is in the tens place (10)
- 0 is in the ones place (0)

2. Write the expanded form:
\[ 9,10,10,510 = 9 \times 9,00,00,000 + 1 \times 10,00,000 + 0 \times 1,00,000 + 1 \times 10,000 + 0 \times 1,000 + 5 \times 100 + 1 \times 10 + 0 \times 1 \]