Question

the planck constant can be written as 6.626070 × 10^(-34). choose the correct exponential notation for plancks constant expressed with three significant figures. a 0.63 × 10^(-34) j·s b 6.02 × 10^(34) j·s c 6.62 × 10^(34) j·s d 6.622 × 10^(-34) j

Explanation:

Step1: Identify significant figures

The given Planck's constant is $6.626070\times 10^{-34}$. We need 3 significant - figures.

Step2: Round the number

Rounding $6.626070$ to 3 significant figures gives $6.63$. But this is incorrect as when rounding $6.626070$, since the digit after the second 2 is 6 (which is greater than 5), we round up the second 2 to 3. However, in scientific notation for Planck's constant, the correct value with 3 significant figures is $6.63$ is wrong. The correct rounding of $6.626070$ to 3 significant figures following proper scientific - notation rules for Planck's constant gives $6.62\times 10^{-34}$ (because the digit to be dropped is 6 and we are in scientific notation context where we keep the exponent as $- 34$).

Answer:

None of the provided options are correct. The correct exponential notation for Planck's constant with three significant figures is $6.63\times 10^{-34}$ (if we follow normal rounding rules for a number not in a context - specific scientific notation where the standard value of Planck's constant is well - known to be around $6.626\times 10^{-34}$ and when rounded to 3 significant figures is $6.63\times 10^{-34}$; if we consider the more accurate scientific - notation for Planck's constant with 3 significant figures it should be $6.62\times 10^{-34}$). If we assume there is a mis - typing in the options and we go with the closest correct - looking one in terms of significant figures and exponent, we note that the correct form should have an exponent of $-34$ and 3 significant figures. The closest option in terms of significant figures and the correct exponent is not among the given ones. If we had to choose the best wrong option based on significant figures and the correct exponent sign, we would note that option a has the wrong coefficient value ($0.63\times 10^{-34}$ is not correct scientific notation as the coefficient should be between 1 and 10), option b and c have the wrong exponent sign ($10^{34}$ instead of $10^{-34}$), and option d has 4 significant figures ($6.622$). But if we assume a minor error in the options and we focus on the exponent and the general form, the closest in terms of having the correct exponent and trying to get the right number of significant figures (even though not exactly correct) would be if we consider a correction in the coefficient of option a to be $6.63\times 10^{-34}$ (but this is still not exactly correct as the correct rounded value of the Planck's constant coefficient to 3 significant figures considering its actual value is $6.63$). In a strict sense, none of the options are correct.