How much greater is 3, point, 8, times, 10, to the power minus 53.8×10 
−5
  than 2, point, 2, times, 10, to the power minus 82.2×10 
−8
 ? Express your answer using either standard notation or scientific notation.

We are tasked with comparing two numbers expressed in scientific notation and determining how much greater one is than the other.

Let's break the problem into two parts:

1. **First number**: \( 3.8 \times 10^{-53.8 \times 10^{-5}} \)
2. **Second number**: \( 2.2 \times 10^{-82.2 \times 10^{-8}} \)

### Step 1: Simplify the Exponents
For both numbers, we need to simplify the exponents.

#### For the first number:
\[
-53.8 \times 10^{-5} = -0.000538
\]
So, the first number becomes:
\[
3.8 \times 10^{-0.000538}
\]

#### For the second number:
\[
-82.2 \times 10^{-8} = -0.000000822
\]
So, the second number becomes:
\[
2.2 \times 10^{-0.000000822}
\]

### Step 2: Subtract the two numbers
Now we will calculate the difference between these two values to determine how much greater the first number is than the second.

Let's approximate the results using logarithmic rules to calculate the exact difference.The first number \( 3.8 \times 10^{-0.000538} \) is approximately 3.795, while the second number \( 2.2 \times 10^{-0.000000822} \) is approximately 2.200. 

The difference between the two numbers is about \( 1.595 \). Therefore, the first number is approximately 1.595 greater than the second.

Would you like more details or have any

How much greater is 3.8 times 10 to the power minus 53.8×10−5 than 2.2 times 10 to the power minus 82.2×10−8? Express your answer using either standard notation or scientific notation.

Learn how to compare two numbers expressed in scientific notation with negative exponents: 3.8 × 10^(-0.000538) and 2.2 × 10^(-0.000000822). This problem involves simplifying exponents and approximating values using logarithmic rules, suitable for students in Grades 10-12.

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