Express each of the following number in standers from:
( i ) 538
( ii ) 6428000
( iii ) 82934000000
( iv ) 940000000000
( v ) 23000000

Answer

To express each of the given numbers in standard form, we will follow a systematic approach. The standard form of a number is expressed as \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer.

### Step-by-Step Solutions:

**(i) Convert 538 to standard form:**

1. Identify the significant digits: 5, 3, 8.
2. Place the decimal after the first digit (5): \( 5.38 \).
3. Count how many places the decimal has moved to the left to get from 538 to 5.38. It moved 2 places.
4. Therefore, we express this as:
\[ 538 = 5.38 \times 10^2 \]

**(ii) Convert 6428000 to standard form:**

1. Identify the significant digits: 6, 4, 2, 8.
2. Place the decimal after the first digit (6): \( 6.428 \).
3. Count how many places the decimal has moved to the left to get from 6428000 to 6.428. It moved 6 places.
4. Therefore, we express this as:
\[ 6428000 = 6.428 \times 10^6 \]

**(iii) Convert 82934000000 to standard form:**

1. Identify the significant digits: 8, 2, 9, 3, 4.
2. Place the decimal after the first digit (8): \( 8.2934 \).
3. Count how many places the decimal has moved to the left to get from 82934000000 to 8.2934. It moved 10 places.
4. Therefore, we express this as:
\[ 82934000000 = 8.2934 \times 10^{10} \]

**(iv) Convert 940000000000 to standard form:**

1. Identify the significant digits: 9, 4.
2. Place the decimal after the first digit (9): \( 9.4 \).
3. Count how many places the decimal has moved to the left to get from 940000000000 to 9.4. It moved 11 places.
4. Therefore, we express this as:
\[ 940000000000 = 9.4 \times 10^{11} \]

**(v) Convert 23000000 to standard form:**

1. Identify the significant digits: 2, 3.
2. Place the decimal after the first digit (2): \( 2.3 \).
3. Count how many places the decimal has moved to the left to get from 23000000 to 2.3. It moved 7 places.
4. Therefore, we express this as:
\[ 23000000 = 2.3 \times 10^{7} \]

### Summary of Answers:
1. \( 538 = 5.38 \times 10^2 \)
2. \( 6428000 = 6.428 \times 10^6 \)
3. \( 82934000000 = 8.2934 \times 10^{10} \)
4. \( 940000000000 = 9.4 \times 10^{11} \)
5. \( 23000000 = 2.3 \times 10^{7} \)