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Answer :
To find another way to write 186,000 using scientific notation, we need to express the number in the form [tex]\( a \times 10^b \)[/tex], where [tex]\( 1 \leq a < 10 \)[/tex] and [tex]\( b \)[/tex] is an integer.
Here's how we can do it step-by-step:
1. Identify the Significant Figures: First, look at 186,000 as a number. The significant figures here are "1.86" because that's how the number starts when you ignore the trailing zeros.
2. Determine the Power of Ten:
- Count how many places you need to move the decimal point to change 186,000 into 1.86. We need to move it 5 positions to the left.
- This is because we're scaling down from a large number to a smaller number by dividing by 100,000, which means multiplying by [tex]\( 10^5 \)[/tex].
3. Write in Scientific Notation:
- Thus, 186,000 becomes [tex]\( 1.86 \times 10^5 \)[/tex].
4. Compare with the Options:
- Look at the given choices:
- F: [tex]\(1.86 \times 10^3\)[/tex]
- G: [tex]\(186 \times 10^5\)[/tex]
- H: [tex]\(18.6 \times 10^6\)[/tex]
- J: [tex]\(1.86 \times 10^5\)[/tex]
- The correct expression for 186,000 in scientific notation is option J: [tex]\(1.86 \times 10^5\)[/tex].
Therefore, another way to write 186,000 is [tex]\(1.86 \times 10^5\)[/tex], which matches option J.
Here's how we can do it step-by-step:
1. Identify the Significant Figures: First, look at 186,000 as a number. The significant figures here are "1.86" because that's how the number starts when you ignore the trailing zeros.
2. Determine the Power of Ten:
- Count how many places you need to move the decimal point to change 186,000 into 1.86. We need to move it 5 positions to the left.
- This is because we're scaling down from a large number to a smaller number by dividing by 100,000, which means multiplying by [tex]\( 10^5 \)[/tex].
3. Write in Scientific Notation:
- Thus, 186,000 becomes [tex]\( 1.86 \times 10^5 \)[/tex].
4. Compare with the Options:
- Look at the given choices:
- F: [tex]\(1.86 \times 10^3\)[/tex]
- G: [tex]\(186 \times 10^5\)[/tex]
- H: [tex]\(18.6 \times 10^6\)[/tex]
- J: [tex]\(1.86 \times 10^5\)[/tex]
- The correct expression for 186,000 in scientific notation is option J: [tex]\(1.86 \times 10^5\)[/tex].
Therefore, another way to write 186,000 is [tex]\(1.86 \times 10^5\)[/tex], which matches option J.
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