Which of the following numbers is written in the standard form ?

Question

Accepted Answer

Option 3, which is 8.5×10$^{-12}$, is written in the standard form. In scientific notation, a number is in standard form when it is expressed as a product of a number between 1 and 10 and a power of 10. Let's analyze each option to understand why Option 3 is correct and why the others are not.

1. **Option 1: 83.7×10$^{-9}$**
   - This number is not in standard form because the coefficient, 83.7, is not between 1 and 10. For a number to be in standard form, the coefficient must be greater than or equal to 1 and less than 10.

2. **Option 2: 45 × 10$^{3}$**
   - Similar to Option 1, this number is not in standard form because the coefficient, 45, is not between 1 and 10. The coefficient must be adjusted to fall within the range of 1 to 10 for it to be considered standard form.

3. **Option 3: 8.5×10$^{-12}$**
   - This is the correct option because the coefficient, 8.5, is between 1 and 10, which satisfies the requirement for standard form. Additionally, it is multiplied by a power of 10, which is a necessary component of scientific notation.

4. **Option 4: 0.6 × 10$^{15}$**
   - This number is not in standard form because the coefficient, 0.6, is less than 1. For a number to be in standard form, the coefficient must be at least 1 and less than 10.

In conclusion, Option 3 is the only choice that meets the criteria for standard form in scientific notation, with a coefficient between 1 and 10 and a power of 10. This is why it is the correct answer.