To divide the numbers 0.075 and 0.030, we will perform the calculation step-by-step, and then we'll identify the result with the correct number of significant digits.
Step 1: Perform the Division
Calculate \( \frac{0.075}{0.030} \):
- Calculating: \[ \frac{0.075}{0.030} = 2.5 \]
Step 2: Determine Significant Digits
Identifying significant digits:
-
In the number 0.075:
- The leading zeros are not significant, so we only count the digits after the leading zeros.
- The digits 75 are significant.
- Therefore, 0.075 has 2 significant digits.
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In the number 0.030:
- The leading zero is not significant, but the zero after the 3 counts as significant because it is after a non-zero digit.
- The digits 30 (including the trailing zero) are significant.
- Therefore, 0.030 has 2 significant digits.
Step 3: Determine the Final Result with Correct Significant Digits
When performing mathematical operations (like division), the result should be reported with the same number of significant digits as the measurement with the fewest significant digits involved in the calculation.
- Both numbers (0.075 and 0.030) have 2 significant digits.
Final Result
The calculated answer from the division is 2.5. However, since both original numbers have 2 significant digits, we need to express our answer in 2 significant digits.
Thus, we round 2.5 to 2 significant digits, resulting in:
\[ \text{Final Answer: } 2.5 \]
Summary
- Calculator Answer: \( 2.5 \)
- Significant Digits Answer: \( 2.5 \)
- Number of Significant Digits: 2
So the answer, keeping significant figures in mind, remains \( 2.5 \).