If p = (12·34 × 10$^{10}$) – (5·67 × 10$^{9}$), then p is expressed in standard form as :

Question

Accepted Answer

To determine why Option 1 is the correct answer, we need to evaluate the expression $ p = (12.34 \times 10^{10}) - (5.67 \times 10^{9}) $ and express the result in standard form.

### Step-by-Step Calculation:

1. **Express Both Terms with the Same Power of 10:**
   - The first term is already in the form $ 12.34 \times 10^{10} $.
   - Convert the second term to the same power of 10: 
     $$
     5.67 \times 10^{9} = 0.567 \times 10^{10}
     $$

2. **Subtract the Terms:**
   - Now, subtract the second term from the first:
     $$
     (12.34 \times 10^{10}) - (0.567 \times 10^{10}) = (12.34 - 0.567) \times 10^{10}
     $$
   - Calculate the subtraction:
     $$
     12.34 - 0.567 = 11.773
     $$
   - Therefore, the expression becomes:
     $$
     11.773 \times 10^{10}
     $$

3. **Convert to Standard Form:**
   - To express $ 11.773 \times 10^{10} $ in standard form, adjust it to have a single digit before the decimal point:
     $$
     1.1773 \times 10^{11}
     $$

### Explanation of Options:

- **Option 1: $ 1.1773 \times 10^{11} $**
  - This matches our calculated result, confirming it as the correct answer.

- **Option 2: $ 1.1773 \times 10^{10} $**
  - This option incorrectly represents the power of 10. The correct power should be $ 10^{11} $ after adjusting the decimal point.

- **Option 3: $ 1.773 \times 10^{11} $**
  - This option has an incorrect coefficient. The correct coefficient is 1.1773, not 1.773.

- **Option 4: $ 1.773 \times 10^{10} $**
  - This option is incorrect both in the coefficient and the power of 10. The correct coefficient is 1.1773, and the power should be $ 10^{11} $.

In conclusion, Option 1 is the correct answer because it accurately represents the expression $ p $ in standard form, following the necessary calculations and adjustments.