Worksheet: Combining Uncertainties

In this worksheet, we will practice finding the uncertainties in the values of quantities that can be calculated from two or more measured values.


A wire carries a current of 2±0.1A for a time of 40±0.5s. What is the percent uncertainty of the charge that passes through the wire in that time?

  • A5%
  • B0.0625%
  • C60%
  • D6.25%
  • E0.6%


Three objects have masses of 3±0.1kg, 7±0.1kg, and 4±0.05kg. What is the uncertainty in the total mass of the three objects?


Cupronickel is an alloy made of copper and nickel. If 10±0.1kg of cupronickel contains 7.5±0.1kg of copper, what is the uncertainty in the amount of nickel it contains?


An iron block has a mass of 20±0.5kg. The acceleration due to gravity is 9.8±0.1/ms. What is the uncertainty in the weight of the block?


An object has a mass of 2±0.1kg and is moving at a speed of 3±0.1/ms. What is the uncertainty in the kinetic energy of the object? Start by calculating the uncertainty in 𝑣, and then calculate the uncertainty in 12𝑚𝑣.


A force of 200±2N is applied to an object with a mass of 10±0.1kg. What is the uncertainty in the acceleration of the object?

  • A2 m/s2
  • B0.4 m/s2
  • C40 m/s2
  • D0.2 m/s2
  • E0.02 m/s2


Two resistors that are in series in a circuit have a combined resistance of 120±0.5Ω. One of the resistors, with a resistance of 30±0.1Ω, is removed. What is the uncertainty in the resistance of the remaining resistor?


A resistor in a circuit has a resistance of 50±1Ω. The current through the resistor is 0.16±0.01A. Work out the potential difference across the resistor as well as the percent uncertainty in this value.

  • A8±8.25%
  • B8±0.16%
  • C8±4.14%
  • D8±0.66%
  • E8±1.01%


In an experiment, a quantity 𝑥 is found to have a value of 4±0.1. What is the uncertainty in 𝑥?


A scientist must mix the correct volumes of two liquids, liquid A and liquid B, as part of an experiment. He must mix 500 mL of liquid A with 200 mL of liquid B. He uses a measuring cylinder to measure the volume of each liquid first. The measuring cylinder has a resolution of 5 mL. He then mixes the two liquids. What is the uncertainty in the volume of the mixture?


In an experiment, a quantity 𝑞 is found to have a value of 15±0.3. What is the percent uncertainty in 𝑞?

  • A0.09%
  • B0.6%
  • C4%
  • D2%
  • E9%


Two resistors have resistances of 20±0.1Ω and 80±0.2Ω. If the two resistors were placed in series, what would the uncertainty of the two resistors together be?


An object moves along a straight line at a speed of 2±0.1/ms for 20±0.5s. Work out the distance that the object moves as well as the uncertainty in this value.

  • A40±0.075m
  • B40±3m
  • C40±0.6m
  • D40±1.09m
  • E40±1.65m


A sound wave travels through a medium with a speed of 360/±9%ms. The wavelength of the sound wave is 2±2%m. What is the percent uncertainty in the frequency of the sound wave?

  • A4.5%
  • B1.025%
  • C7%
  • D11%
  • E18%

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