Sure, let’s break down how to express the mass of Mars, [tex]\(642,000,000,000,000,000,000,000\)[/tex] kg, in scientific notation.
1. Understand Scientific Notation:
- Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of 10.
- The general form is [tex]\(a \times 10^b\)[/tex], where [tex]\(1 \leq a < 10\)[/tex] and [tex]\(b\)[/tex] is an integer.
2. Convert the Given Number:
- The given number is [tex]\(642,000,000,000,000,000,000,000\)[/tex] kg.
- We need to convert this to a form where it’s a number between 1 and 10 multiplied by a power of 10.
3. Identify the Leading Digit:
- The leading digits of [tex]\(642,000,000,000,000,000,000,000\)[/tex] are 6.42.
4. Count the Decimal Places:
- To get from [tex]\(642,000,000,000,000,000,000,000\)[/tex] to 6.42, we need to count how many places we move the decimal point to the left.
- Moving the decimal point 23 places to the left converts [tex]\(642,000,000,000,000,000,000,000\)[/tex] to [tex]\(6.42\)[/tex].
5. Form the Scientific Notation:
- Thus, moving the decimal 23 places gives us the power of 10.
- Hence, the number in scientific notation is [tex]\(6.42 \times 10^{23}\)[/tex].
6. Verify the Options:
- Option A: [tex]\(0.642 \times 10^{21}\)[/tex] – Incorrect, wrong form and wrong exponent.
- Option B: [tex]\(6.42 \times 10^{23}\)[/tex] – Correct, matches our calculation.
- Option C: [tex]\(0.642^{24}\)[/tex] – Incorrect, improper notation.
- Option D: [tex]\(0.642 \times 10^{24}\)[/tex] – Incorrect, does not have the correct leading digits nor exponent.
So, the correct answer is:
B. [tex]\(6.42 \times 10^{23}\)[/tex] kg
