To solve the division problem \(0.2 \div 0.0005\) and to determine the significant digits, let’s go through the steps clearly.
Step 1: Perform the Calculation
Let's do the division:
\[ 0.2 \div 0.0005 \]
To make the calculation easier, we can express both numbers in scientific notation:
- \(0.2 = 2.0 \times 10^{-1}\)
- \(0.0005 = 5.0 \times 10^{-4}\)
Now, we substitute these values into the division:
\[ \frac{2.0 \times 10^{-1}}{5.0 \times 10^{-4}} \]
Step 2: Simplify
Now we divide the coefficients and subtract the exponents of ten:
\[ \frac{2.0}{5.0} = 0.4 \] And for the exponents: \[ 10^{-1} \div 10^{-4} = 10^{-1 - (-4)} = 10^{-1 + 4} = 10^{3} \]
So putting it all together:
\[ 0.4 \times 10^{3} = 4.0 \times 10^{2} \]
Thus, the answer to the calculation is:
\[ 4.0 \times 10^{2} = 400 \]
Step 3: Identify Significant Digits
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Identify the significant digits in the original numbers:
- For \(0.2\): This number has 1 significant digit (the "2").
- For \(0.0005\): This number has 1 significant digit (the "5").
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Determine the significant digits in the result:
- Since the fewest number of significant digits among the numbers we divided is 1, the result must also be expressed with 1 significant digit. Thus, we round \(400\) down to 400, not counting the zeroes after the \(4\) since they don't contribute significant value.
Final Answer
- Calculator Answer: \(400\)
- Significant Digits Answer: \(400\)
- Number of Significant Digits: \(1\)
In summary: The final answer is 400 with 1 significant digit.