Simplify : `(4xx10^(-2))-(2.5xx10^(-3))`

Answer

To simplify the expression `(4 × 10^(-2)) - (2.5 × 10^(-3))`, we can follow these steps:

### Step 1: Rewrite the terms using decimal notation
We know that \(10^{-a} = \frac{1}{10^a}\). Therefore, we can rewrite the terms:
- \(4 × 10^{-2} = 4 × \frac{1}{10^2} = 4 × \frac{1}{100} = 0.04\)
- \(2.5 × 10^{-3} = 2.5 × \frac{1}{10^3} = 2.5 × \frac{1}{1000} = 0.0025\)

### Step 2: Set up the subtraction
Now we can rewrite our original expression:
\[ 0.04 - 0.0025 \]

### Step 3: Align the decimal points
To perform the subtraction, we need to align the decimal points. It helps to have the same number of decimal places:
\[ 0.0400 - 0.0025 \]

### Step 4: Perform the subtraction
Now we can subtract:
- Start from the rightmost digit:
- \(0 - 5\): We need to borrow, so we take 1 from the next column (which is 4, making it 3), and now we have \(10 - 5 = 5\).
- Next column: \(3 - 2 = 1\).
- Next column: \(4 - 0 = 4\).

Putting it all together, we get:
\[ 0.0400 - 0.0025 = 0.0375 \]

### Final Answer
The simplified result is:
\[ 0.0375 \]

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