Given the numbers `3.75xx10^(-7), 3 3/4xx10^(-7), 375xx10^(-9)` and `3/8xx10^(-7)`. Which of these is not equal to 0.000000375?

Options

A. `3 3/4xx10^(-7)`
B. `375xx10^(-9)`
C. `3/8xx10^(-7)`
D. `3.75xx10^(-7)`

Answer

To determine which of the given numbers is not equal to 0.000000375, we will convert each number into decimal form and compare it with 0.000000375.

### Step 1: Convert `3.75 x 10^(-7)` to decimal
To convert this number, we move the decimal point 7 places to the left (because of the negative exponent).

- Start with 3.75.
- Move the decimal point 7 places to the left:
- 1st move: 0.375
- 2nd move: 0.0375
- 3rd move: 0.00375
- 4th move: 0.000375
- 5th move: 0.0000375
- 6th move: 0.00000375
- 7th move: 0.000000375

So, `3.75 x 10^(-7) = 0.000000375`.

### Step 2: Convert `3 3/4 x 10^(-7)` to decimal
First, convert the mixed number to an improper fraction:
- \(3 \frac{3}{4} = \frac{15}{4}\).

Now, convert it to decimal:
- \( \frac{15}{4} = 3.75\).

Now, move the decimal point 7 places to the left:
- Following the same process as above, we find:
- `3.75 x 10^(-7) = 0.000000375`.

### Step 3: Convert `375 x 10^(-9)` to decimal
Here, we move the decimal point 9 places to the left:
- Start with 375.
- Move the decimal point 9 places to the left:
- 1st move: 37.5
- 2nd move: 3.75
- 3rd move: 0.375
- 4th move: 0.0375
- 5th move: 0.00375
- 6th move: 0.000375
- 7th move: 0.0000375
- 8th move: 0.00000375
- 9th move: 0.000000375

So, `375 x 10^(-9) = 0.000000375`.

### Step 4: Convert `3/8 x 10^(-7)` to decimal
First, convert \( \frac{3}{8} \) to decimal:
- \( \frac{3}{8} = 0.375 \).

Now, move the decimal point 7 places to the left:
- Start with 0.375.
- Move the decimal point 7 places to the left:
- 1st move: 0.0375
- 2nd move: 0.00375
- 3rd move: 0.000375
- 4th move: 0.0000375
- 5th move: 0.00000375
- 6th move: 0.000000375
- 7th move: 0.0000000375

So, `3/8 x 10^(-7) = 0.0000000375`.

### Conclusion
Now we compare all the converted values:
- `3.75 x 10^(-7) = 0.000000375`
- `3 3/4 x 10^(-7) = 0.000000375`
- `375 x 10^(-9) = 0.000000375`
- `3/8 x 10^(-7) = 0.0000000375` (This is not equal to 0.000000375)

Thus, the number that is not equal to 0.000000375 is **`3/8 x 10^(-7)`**.