Rewrite the following result in its clearest forms (Best Estimate ± Uncertainty) and scientific notation, with suitable numbers of significant figures in the uncertainty and decimal places in the best estimate:

𝑣
=
(
238965
±
47
)
𝑚
/
𝑠
=

Question

Rewrite the following result in its clearest forms (Best Estimate ± Uncertainty) and scientific notation, with suitable numbers of significant figures in the uncertainty and decimal places in the best estimate:

𝑣
=
(
238965
±
47
)
𝑚
/
𝑠
=

BlackTom AI · Accepted Answer

We are given the result v = (238965 ± 47) m/s and asked to rewrite it in clearest form using scientific notation with an appropriate number of significant figures in the uncertainty and decimal places in the best estimate.
Option 1: (2.389 ± 0.005) × 10^5 m/s
- Here, the best estimate is 2.389 with three decimal places, but the uncertainty is 0.005, which corresponds to the 3rd decimal place. Since the original uncertainty is 47 on a base value around 238,000, the relative precision is quite small and the uncertainty should reflect more digits in the same scale as the best estimate. The combination (2.389 ± 0.005) × 10^5 would imply rounding the best value to three decimals and the uncertainty to a thousandth, which does not align with the actual uncertainty 47 on 238965. This option underreports the precision of the best estimate relative to the given uncertainty and uses an unnecessarily rounded uncertainty.
Option 2: (2.3897 ± 0.0005) × 10^5 m/s
- The best estimate 2.3897 has four decimal places, and the uncertainty 0.0005 has its least significant digit at the 4th decimal place (10^-4). This pairing mirrors the magnitude of the original uncertainty (47 on ~2.39×10^5), giving a consistent representation in scientific notation. Rounding the central value to four decimals yields 2.3897, and expressing the uncertainty as 0.0005 keeps two significant digits in the scale of 10^-4 while not overstating precision. This option is consistent with standard practice: maintain the same order of magnitude for the uncertainty and align the decimal places of the best estimate accordingly.
Option 3: (2.4 ± 0.5) × 10^5 m/s
- This choice reduces both the best estimate and the uncertainty to only one significant figure beyond the leading digits, which is far too coarse given the original data (238965 ± 47). It destroys useful precision and misrepresents the measurement by collapsing many digits into a rough 2.4 × 10^5 with ±0.5 × 10^5, effectively replacing the meaningful digits with a broad band. This is not an appropriate fit for the provided values.
Option 4: (2.3897 ± 0.0047) × 10^5 m/s
- Although the central value 2.3897 is reasonable, the uncertainty 0.0047 corresponds to four significant digits but places the least significant digit at the 4th decimal in a way that does not align with the original ±47 on 238965 when expressed in the same scale. The magnitudes are mismatched: 0.0047 × 10^5 equals 470, which is an order of magnitude larger than the original 47. This overstates the uncertainty and misrepresents the data’s precision.

Summarizing the reasoning across options, option 2 provides the appropriate balance: the central value is expressed with four decimal places in scientific notation, and the uncertainty is expressed with the correct scale and digits to reflect the given data without overstating precision. The other options either understate or overstate the precision, or fail to reflect the proper scale of the uncertainty relative to the best estimate.

SPHY001 Skills Test 1 (LAB 2) | LA024

Rewrite the following result in its clearest forms (Best Estimate ± Uncertainty) and scientific notation, with suitable numbers of significant figures in the uncertainty and decimal places in the best estimate: 𝑣 = ( 238965 ± 47 ) 𝑚 / 𝑠 =

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