Write 0.003 84 in standard form.
The Correct Answer and Explanation is:
To express the number 0.00384 in standard form (also known as scientific notation), we first need to identify its significant figures and then move the decimal point to convert it into a format where it is expressed as a product of a number between 1 and 10 and a power of ten.
Steps to Convert 0.00384 to Standard Form:
- Identify the Significant Figures:
The significant figures in the number 0.00384 are 384. The leading zeros (the zeros before the 3) are not significant; they only serve as placeholders. - Move the Decimal Point:
To convert 0.00384 into a number between 1 and 10, we need to move the decimal point to the right until we have a number in the desired range.
- In this case, we move the decimal point 3 places to the right. So, (0.00384) becomes (3.84).
- Determine the Power of Ten:
Because we moved the decimal point 3 places to the right, we need to express this movement as a negative exponent of 10 (since we are starting with a decimal number that is less than 1).
- Thus, we can express the movement as (10^{-3}).
- Write in Standard Form:
Now we can combine our findings into the standard form:
[
0.00384 = 3.84 \times 10^{-3}
]
Final Answer:
Thus, the standard form of 0.00384 is:
[
3.84 \times 10^{-3}
]
Explanation:
Standard form is a way of expressing numbers that are either very large or very small in a concise manner, making them easier to read and work with, especially in scientific contexts. It involves using powers of ten to scale a number to a more manageable size. This notation is particularly useful in fields like physics and engineering, where measurements can vary dramatically in scale. By converting numbers into standard form, calculations involving multiplication and division become simpler, as you can deal with the base numbers separately from their exponential factors. This method not only enhances clarity but also reduces the potential for errors in calculations, especially when dealing with numerous zeros, as in the case of small decimal values.