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
Problem Analysis 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.
Significant Digits in 4.3 x 10^{-3} mL 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 of the number and does not affect the number of significant digits. Therefore, there are 2 significant digits.
Significant Digits in 72700. kg For the measurement 72700. k g , the digits 7, 2, and 7 are significant. The two zeros are also significant because the number has a decimal point. Therefore, there are 5 significant digits.
Significant Digits in 0.005100 J For the measurement 0.005100 J , the zeros to the left of the 5 are not significant. The digits 5, 1, 0, and 0 are significant. Therefore, there are 4 significant digits.
Significant Digits in -6.0 x 10^{-1} kJ / mol For the measurement − 6.0 × 1 0 − 1 k J / m o l , the minus sign is irrelevant when determining significant digits. The digits 6 and 0 are significant. The term 1 0 − 1 only indicates the magnitude of the number and does not affect the number of significant digits. Therefore, there are 2 significant digits.
Final Answer 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 data. For instance, if you measure the length of a table to be 2.30 meters, using three significant figures indicates that you measured it more precisely than if you reported it as 2.3 meters. In calculations, the result should reflect the least precise measurement used. For example, when calculating the area of a rectangle, if the length is 12.5 cm and the width is 3.4 cm, the area should be reported as 43 cm², not 42.5 cm², because the width has only two significant figures.
The significant digits for the provided measurements are as follows: 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, and − 6.0 × 1 0 − 1 k J / m o l has 2 significant digits. Therefore, the total significant digits are 2, 5, 4, and 2 respectively.
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