What is $2.56 \times 10^{-5}$ in standard form?
A. 0.000256
B. $25,600,000$
C. 256,000
D. 0.0000256
Answer (1)
We are given the number 2.56 × 1 0 − 5 in scientific notation.
To convert to standard form, we multiply 2.56 by 1 0 − 5 .
This is equivalent to moving the decimal point in 2.56 five places to the left.
The standard form of 2.56 × 1 0 − 5 is 0.0000256 .
Explanation
Understanding the Problem We are given a number in scientific notation: 2.56 × 1 0 − 5 . Our goal is to convert this number into standard form, which means writing it as a regular decimal number.
Converting to Standard Form To convert from scientific notation to standard form, we need to multiply 2.56 by 1 0 − 5 . This means we need to move the decimal point in 2.56 five places to the left because the exponent is − 5 .
Moving the Decimal Point Starting with 2.56 , moving the decimal point one place to the left gives us 0.256 . Moving it two places gives us 0.0256 . Moving it three places gives us 0.00256 . Moving it four places gives us 0.000256 . Finally, moving it five places gives us 0.0000256 .
Final Answer Therefore, 2.56 × 1 0 − 5 in standard form is 0.0000256 .
Examples
Scientific notation is useful in many real-world scenarios. For example, in astronomy, the distance to a star might be 3.8 × 1 0 16 meters. In biology, the size of a bacteria might be 1.5 × 1 0 − 6 meters. Converting these numbers to standard form helps us understand their magnitude in a more intuitive way. Similarly, in computer science, very small or very large numbers are often represented using scientific notation.
