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A student measures a boiling water bath with two different thermometers. The digital thermometer records the temperature as 100.2°C and has an uncertainty of 0.1°C. The analog thermometer records the temperature as 99.0°C and has an uncertainty of 0.5°C. What is the percent uncertainty of each thermometer? And what is the percent error given that water boils at 100.0°C?

Sagot :

Answer:

Explanation:

Measurement made = 100.2 °C

uncertainty = 0.1°C

percent uncertainty = .1 x 100 / 100.2

= .099 %

2 nd thermometer :

Measurement made = 99.0 °C

uncertainty = 0.5°C

percent uncertainty = .5 x 100 / 99

= .505  %

Percent error :

1 st thermometer

Error = 100.2 - 100 = .2 °C

measurement = 100.2

percent error = .2 x 100 / 100.2

= .1996 %

2 nd thermometer

Error = 100.00 - 99 = 1.00 °C

measurement = 99

percent error = 1 x 100 / 99

= 1.01  %

  • The percent uncertainty of digital thermometer is 0.099 %. The percent uncertainty of analog thermometer is 0.505%.

  • The percent error of digital thermometer is 0.1996 %. The percent error of analog thermometer is 1.01 %.

Percent uncertainty is the measure of degree of error region with the  uncertainty in the measurement.

The percentage error is the difference in the measurement of the values with actual value.

Computation for percent uncertainty and percent error

The percent uncertainty (%U) is calculated by:

[tex]\% U=\rm \dfrac{Uncertainty}{Measurement}\;\times\;100[/tex]

The percent error (%E)  is calculated by:

[tex]\%E=\rm \dfrac{error\;value-actual\;value}{error\;value}\;\times\;100[/tex]

  • The percent uncertainty and error for digital thermometer is given as:

The Recorded temperature = 100.2 degree Celsius

The actual temperature = 100 degrees Celsius

The uncertainty in the readings is 0.1 degree Celsius

The percent uncertainty is given by:

[tex]\%U=\dfrac{0.1}{100.2}\;\times\;100\\\\ \%U=0.099\;\%[/tex]

The percent uncertainty of digital thermometer is 0.099 %.

The percent error is given by:

[tex]\% E=\dfrac{100.2-100}{100.2}\;\times\;100 \\\\\% E=\dfrac{0.2}{100.2}\;\times\;100\\\\ \% E=0.1996\;\%[/tex]

The percent error of digital thermometer is 0.1996 %.

  • The percent uncertainty and error for analog thermometer is given as:

The Recorded temperature = 99 degree Celsius

The actual temperature = 100 degrees Celsius

The uncertainty in the readings is 0.5 degree Celsius

The percent uncertainty is given by:

[tex]\%U=\dfrac{0.5}{99}\;\times\;100\\\\ \%U=0.505\;\%[/tex]

The percent uncertainty of analog thermometer is 0.505%.

The percent error is given by:

[tex]\% E=\dfrac{100-99}{99}\;\times\;100 \\\\\% E=\dfrac{1}{99}\;\times\;100\\\\ \% E=1.01\;\%[/tex]

The percent error of analog thermometer is 1.01 %.

Learn more about percent error, here:

https://brainly.com/question/3105259

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