Count the significant digits in each of these measurements:
| measurement | number of significant digits |
| :---------------------- | :----------------------------- |
| [tex]$4.3 \times 10^{-3} mL$[/tex] | $\square$ |
| [tex]$72700 . kg$[/tex] | $\square$ |
| 0.005100 J | $\square$ |
| [tex]$-6.0 \times 10^{-1} kJ / mol$[/tex] | $\square$ |
Answer (2)
Count significant digits in 4.3 × 1 0 − 3 m L : 2.
Count significant digits in 72700. k g : 5.
Count significant digits in 0.005100 J : 4.
Count significant digits in − 6.0 × 1 0 − 1 k J / m o l : 2.
2 , 5 , 4 , 2
Explanation
Understanding Significant Digits We are asked to determine the number of significant digits in each of the given measurements. Significant digits are the digits in a number that contribute to the precision of the number. Let's analyze each measurement separately.
Analyzing Measurement 1 For the measurement 4.3 × 1 0 − 3 m L , the digits 4 and 3 are significant. The term 1 0 − 3 only indicates the magnitude and does not affect the number of significant digits. Therefore, there are 2 significant digits.
Analyzing Measurement 2 For the measurement 72700. k g , the digits 7, 2, and 7 are significant. The two trailing zeros are also significant because of the presence of the decimal point. Therefore, there are 5 significant digits.
Analyzing Measurement 3 For the measurement 0.005100 J , the leading zeros (0.00) are not significant. The digits 5 and 1 are significant, and the two trailing zeros are also significant. Therefore, there are 4 significant digits.
Analyzing Measurement 4 For the measurement − 6.0 × 1 0 − 1 k J / m o l , the digit 6 is significant, and the zero after the decimal point is also significant. The negative sign and the term 1 0 − 1 do not affect the number of significant digits. Therefore, there are 2 significant digits.
Final Results In summary:
4.3 × 1 0 − 3 m L has 2 significant digits.
72700. k g has 5 significant digits.
0.005100 J has 4 significant digits.
− 6.0 × 1 0 − 1 k J / m o l has 2 significant digits.
Examples
Significant figures are crucial in scientific measurements to accurately represent the precision of a value. For example, if you measure the length of a table to be 2.30 meters, indicating three significant figures, it implies that you have measured the length to the nearest centimeter. This level of precision is important in calculations and data analysis to avoid overstating the accuracy of your results. In engineering, using correct significant figures ensures that designs and calculations are based on reliable data, preventing potential errors in construction or manufacturing.
The significant digits for the measurements are as follows: 4.3 × 1 0 − 3 m L has 2 digits, 72700. k g has 5 digits, 0.005100 J has 4 digits, and − 6.0 × 1 0 − 1 k J / m o l has 2 digits. The final counts are 2, 5, 4, 2 respectively.
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