To multiply two numbers and express the answer with the correct number of significant digits, let's follow these steps for the calculation:
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Calculator Calculation: Perform the multiplication using a calculator: \[ 0.00036 \times 0.02 = 0.0000072 \]
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Determining Significant Digits: Next, we need to identify the number of significant digits in each number:
- For 0.00036: The leading zeros are not significant. The significant digits are "36", which gives us 2 significant digits.
- For 0.02: The leading zero is not significant. The significant digit is "2", which gives us 1 significant digit.
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Identifying the Limiting Factor: According to the rules of significant digits, the result of a multiplication should have the same number of significant digits as the factor with the least significant digits. In this case, 0.02 has the least at 1 significant digit.
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Rounding the Result: The calculator gives us \(0.0000072\), but since we need to express our answer with 1 significant digit, we round \(0.0000072\):
- The first significant digit is "7".
- Keeping only 1 significant digit, we can express our answer as \(0.000007\), since \(0.000007\) reflects the number rounded to the appropriate significant digits place.
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Final Answer: So, the final answer is: \[ 0.000007 \]
- Calculated Answer: \(0.0000072\)
- Significant Digits Answer: \(0.000007\)
- Number of Significant Digits: 1
This clearly outlines the process of multiplication, identifying significant figures, rounding the answer, and presenting the final result.
1 answer