0.205-0.2014 can be expressed as

Options

A. `0.0036`
B. `3.6xx10^(-3)`
C. `4.0xx10^(-3)`
D. `4xx10^(-3)`

Answer

To solve the problem \(0.205 - 0.2014\) and express the result in standard format, we can follow these steps:

### Step 1: Perform the Subtraction
We start by subtracting \(0.2014\) from \(0.205\).

\[ 0.205 - 0.2014 \]

To do this, we align the numbers by their decimal points:

```
0.2050
- 0.2014
```

### Step 2: Subtract Digit by Digit
Now, we subtract each column starting from the rightmost side:

- In the thousandths place: \(0 - 4\) (we cannot subtract, so we borrow)
- Borrow 1 from the hundredths place (which becomes \(4\)), making the thousandths place \(10\).
- Now, \(10 - 4 = 6\).

- In the hundredths place: \(4 - 1 = 3\).

- In the tenths place: \(0 - 0 = 0\).

- In the units place: \(2 - 2 = 0\).

Putting it all together, we get:

\[ 0.205 - 0.2014 = 0.0036 \]

### Step 3: Determine Significant Figures
Next, we need to express \(0.0036\) in standard format.

- The number \(0.205\) has 3 significant figures.
- The number \(0.2014\) has 4 significant figures.

The result \(0.0036\) has 2 significant figures. However, we need to express the answer with the least number of significant figures from the original numbers, which is 3.

### Step 4: Convert to Standard Form
To express \(0.0036\) in standard form, we shift the decimal point to the right until we have a number between 1 and 10:

\[ 0.0036 = 3.6 \times 10^{-3} \]

### Final Answer
Thus, the final answer is:

\[ 3.6 \times 10^{-3} \]