`(24.69 xx 10 ^(10)) - ( 13.58 xx 10 ^(8)) ` is expressed in standard form as

Options

A. `2455.42 x xx 10 ^(8)`
B. `2.45542 xx 10 ^(11)`
C. `245542 xx 10^(9)`
D. `24.5542 xx 10 ^(8)`

Answer

To solve the expression \( (24.69 \times 10^{10}) - (13.58 \times 10^{8}) \) and express it in standard form, we will follow these steps:

### Step 1: Rewrite the numbers in a comparable format
We need to express both numbers with the same power of 10. We can convert \( 24.69 \times 10^{10} \) into a form that has \( 10^8 \) as the base.

\[ 24.69 \times 10^{10} = 24.69 \times 10^{10 - 2} \times 10^2 = 2469 \times 10^{8} \]

### Step 2: Rewrite the expression
Now we can rewrite the entire expression using the same power of 10:

\[ (2469 \times 10^{8}) - (13.58 \times 10^{8}) \]

### Step 3: Factor out the common term
Since both terms now have \( 10^{8} \) as a common factor, we can factor it out:

\[ = (2469 - 13.58) \times 10^{8} \]

### Step 4: Perform the subtraction
Now we perform the subtraction:

\[ 2469 - 13.58 = 2455.42 \]

### Step 5: Write the final expression
Now we can write the final expression in standard form:

\[ = 2455.42 \times 10^{8} \]

### Conclusion
Thus, the expression \( (24.69 \times 10^{10}) - (13.58 \times 10^{8}) \) expressed in standard form is:

\[ \boxed{2455.42 \times 10^{8}} \]

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