Is `10.342xx10^(7)` the standard form of a large number ?

Answer

To determine if \( 10.342 \times 10^7 \) is in standard form for a large number, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Standard Form**: The standard form (or scientific notation) of a number is expressed as \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer.

2. **Identify the Given Number**: The given number is \( 10.342 \times 10^7 \).

3. **Check the Coefficient**: The coefficient here is \( 10.342 \). We need to check if it falls within the range of \( 1 \) to \( 10 \):
- Since \( 10.342 \) is greater than \( 10 \), it does not satisfy the condition \( 1 \leq a < 10 \).

4. **Adjust the Coefficient**: To convert \( 10.342 \) into standard form:
- Move the decimal point one place to the left, which gives us \( 1.0342 \).
- This means we need to increase the exponent of \( 10 \) by \( 1 \) (since we moved the decimal left), changing \( 10^7 \) to \( 10^8 \).

5. **Rewrite in Standard Form**: Now we can rewrite the expression:
\[ 10.342 \times 10^7 = 1.0342 \times 10^8 \]

6. **Conclusion**: The expression \( 10.342 \times 10^7 \) is not in standard form because the coefficient \( 10.342 \) is not between \( 1 \) and \( 10 \). The correct standard form is \( 1.0342 \times 10^8 \).

### Final Answer:
No, \( 10.342 \times 10^7 \) is not in standard form of a large number. The standard form is \( 1.0342 \times 10^8 \).