Answer :

To convert the number [tex]7.5 \times 10^{-6}[/tex] into standard notation, follow these steps:

  1. Understand Scientific Notation: The expression [tex]7.5 \times 10^{-6}[/tex] is written in scientific notation. Scientific notation is a way to express very large or very small numbers and consists of a number (called the coefficient) multiplied by a power of 10. In this case, [tex]7.5[/tex] is the coefficient and [tex]10^{-6}[/tex] indicates the power of 10.

  2. Interpret the Exponent: The exponent [tex]-6[/tex] means that you need to move the decimal point in the number [tex]7.5[/tex] six places to the left. Each movement to the left reduces the magnitude of the number by a factor of 10.

  3. Move the Decimal Point: Start with the number 7.5. Move the decimal point six places to the left. If there aren't enough digits, add zeros.

    • Start: [tex]7.5[/tex]
    • Move 1: [tex]0.75[/tex]
    • Move 2: [tex]0.075[/tex]
    • Move 3: [tex]0.0075[/tex]
    • Move 4: [tex]0.00075[/tex]
    • Move 5: [tex]0.000075[/tex]
    • Move 6: [tex]0.0000075[/tex]

  4. Result: After moving the decimal point six places to the left, the number [tex]7.5 \times 10^{-6}[/tex] is expressed in standard notation as [tex]0.0000075[/tex].

By converting scientific notation to standard notation, we are able to see the full numerical value, making it easier to understand the magnitude of very small numbers.

Other Questions