A calculator displays 9.58E-5. How do you write 9,58E-5 in standard form?
The correct answer and explanation is:
The number 9.58E-5 is written in scientific notation, where “E” stands for “times ten raised to the power of”. The “E-5” means that the decimal point in 9.58 should be moved five places to the left.
To convert this into standard form, follow these steps:
- Start with the number 9.58.
- Move the decimal point five places to the left, because of the -5 exponent on the ten.
- Moving the decimal point five places to the left, you get 0.0000958.
Thus, 9.58E-5 in standard form is 0.0000958.
Explanation of Scientific Notation:
Scientific notation is used to express very large or very small numbers in a more concise format. The notation 9.58E-5 represents 9.58 × 10^-5, which indicates that the number is very small and needs to be shifted to the left by five decimal places.
- The E in scientific notation stands for the exponent, which tells you how many places to move the decimal point.
- A positive exponent means the decimal point moves to the right (making the number larger), while a negative exponent means the decimal point moves to the left (making the number smaller).
This method of writing numbers is especially useful in fields like science and engineering, where extremely large or small quantities are common. For example, the size of atoms or the distance between stars is often expressed using scientific notation.