Question

One fluid ounce is equivalent to 0.0078125 US liquid gallon. How do you write 0.0078125 in scientific notation?

A. 7.8125×10⁻³
B. 7.8125×10⁻²
C. 7.8125×10⁻⁴
D. 7.8125×10⁻⁵

Answer 1

To write 0.0078125 in scientific notation, we move the decimal point three places to the right, making it 7.8125, and since we shifted the decimal to the right, we use a negative exponent of -3; hence, the scientific notation is 7.8125×10⁻³.

Step-by-step explanation:

The question asks to express the number 0.0078125 in scientific notation. To convert this number into scientific notation, the decimal point must be moved so that there's only one non-zero digit to the left of the decimal. Since the original number is less than one, moving the decimal point three places to the right gets us 7.8125.

For every place that the decimal is moved, the exponent decreases by one. Since we moved the decimal three places, the exponent will be -3, making the scientific notation 7.8125×10⁻³.

To write the number 0.0078125 in scientific notation, we need to express it as a number between 1 and 10 multiplied by a power of 10. In this case, we can express 0.0078125 as 7.8125 x 10^-3. Therefore, the correct answer is A. 7.8125 x 10^-3.