Convert 0.0000456 to scientific notation.
A. $4.56 \times 10^{-3}$
B. $4.56 \times 10^{-6}$
C. $4.56 \times 10^{-4}$
D. $4.56 \times 10^{-5}$
Answer (2)
Move the decimal point in 0.0000456 to the right until there is one non-zero digit to the left of the decimal point, resulting in 4.56.
Count the number of places the decimal point was moved (5 places) and assign the negative of this number as the exponent of 10, which is -5.
Write the number in scientific notation as 4.56 × 1 0 − 5 .
The final answer is 4.56 × 1 0 − 5 .
Explanation
Understanding Scientific Notation We are asked to convert the number 0.0000456 into scientific notation. Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is typically written as a × 1 0 b , where 1 ≤ ∣ a ∣ < 10 and b is an integer.
Moving the Decimal Point To convert 0.0000456 to scientific notation, we need to move the decimal point to the right until we have a number between 1 and 10. In this case, we move the decimal point 5 places to the right to get 4.56.
Determining the Exponent Since we moved the decimal point 5 places to the right, the exponent of 10 will be -5. This is because we are making the number smaller, so we need a negative exponent to compensate.
Final Result Therefore, 0.0000456 in scientific notation is 4.56 × 1 0 − 5 .
Examples
Scientific notation is incredibly useful in fields like astronomy and chemistry, where dealing with extremely large or small numbers is common. For instance, the distance to a nearby star might be 4.56 x 10^16 meters, and the size of an atom might be 4.56 x 10^-11 meters. Using scientific notation makes these numbers easier to handle and compare.
The number 0.0000456 is converted to scientific notation as 4.56 × 1 0 − 5 . This is done by moving the decimal point 5 places to the right and assigning a negative exponent. The chosen answer is D: 4.56 × 1 0 − 5 .
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