To determine whether the number 1234000 in scientific notation is equal to [tex]\(1.234 \times 10^5\)[/tex], let's break this down step by step:
1. Identify the given number: The given number is 1234000.
2. Convert the given number to scientific notation:
- Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
- In scientific notation, a number is written as [tex]\(a \times 10^n\)[/tex], where [tex]\(1 \leq a < 10\)[/tex] and [tex]\(n\)[/tex] is an integer.
3. Determine the decimal equivalent:
- Let's express 1234000 in the form [tex]\(a \times 10^n\)[/tex].
- We need to express 1234000 as a number between 1 and 10 multiplied by a power of 10.
- 1234000 can be written as [tex]\(1.234 \times 10^6\)[/tex] because if you move the decimal point 6 places to the left, you get 1.234, which is within the range [tex]\([1, 10)\)[/tex].
4. Compare the powers of ten:
- According to the problem statement, it claims that [tex]\(1234000 = 1.234 \times 10^5\)[/tex].
- However, from our conversion, [tex]\(1234000\)[/tex] is equal to [tex]\(1.234 \times 10^6\)[/tex].
5. Conclusion:
- The correct scientific notation for 1234000 is [tex]\(1.234 \times 10^6\)[/tex], not [tex]\(1.234 \times 10^5\)[/tex].
Therefore, the statement that "The number 1234000 in scientific notation is equal to [tex]\(1.234 \times 10^5\)[/tex]" is False (F).
