The weight of one of the smaller species of butterflies was measured at 0.0007 ounces. Write the weight of this butterfly in scientific notation.
The Correct Answer and Explanation is:
The weight of the butterfly is given as 0.0007 ounces. To express this in scientific notation, we need to convert it into a form that uses powers of 10.
Steps:
- Move the decimal point: In this case, the decimal point is placed after the first non-zero digit (7). So, we move the decimal point 4 places to the right.
- 0.0007 becomes 7.0.
- Determine the exponent: The decimal point was moved 4 places to the right, so the exponent for 10 will be -4. This indicates that the number is less than 1, and the decimal point was moved to the right to obtain a smaller value.
Thus, the number 0.0007 can be written in scientific notation as: 7.0×10−47.0 \times 10^{-4}7.0×10−4
Explanation:
- Scientific notation is a shorthand way of expressing very large or very small numbers. It helps to make these numbers more manageable and easier to work with.
- The format for scientific notation is a×10ba \times 10^ba×10b, where aaa is a number between 1 and 10 (called the coefficient), and bbb is an integer (called the exponent).
- The coefficient in this case is 7.0, and the exponent is -4, indicating the number is a small value, 0.0007 ounces, but written in a more compact form.
So, the scientific notation for the butterfly’s weight is 7.0×10−47.0 \times 10^{-4}7.0×10−4 ounces.
