Worksheet: Upper and Lower Bounds

In this worksheet we will practice calculating the maximum and minimum possible values of a measurement.

Q1:

A paper has a length of 11 cm, measured to the nearest 1 mm. What are the upper and lower bounds?

  • ALower bound = 12.95 cm, upper bound = 13.05 cm
  • BLower bound = 11.1 cm, upper bound = 10.9 cm
  • CLower bound = 10.95 cm, upper bound = 11.05 cm
  • DLower bound = 11.05 cm, upper bound = 10.95 cm
  • ELower bound = 10.9 cm, upper bound = 11.1 cm

Q2:

A box has weight 𝑊 of 24 kg to the nearest 1 kg. What is its error interval?

  • A23.5𝑊24.5kgkg
  • B23.5𝑊<24.5kgkg
  • C23𝑊<25kgkg
  • D23.5<𝑊24.5kgkg
  • E23𝑊25kgkg

Q3:

An electrical cable has length 𝐿 of 122 cm to the nearest 1 cm. What is its error interval?

  • A121.5𝐿122.5cmcm
  • B121𝐿123cmcm
  • C121.5<𝐿122.5cmcm
  • D121.5𝐿<122.5cmcm
  • E121𝐿<123cmcm

Q4:

A rectangle has a base of 5 cm to the nearest 1 mm and a height of 2 cm to the nearest 1 mm. Write down the error interval that represents the possible area, 𝐴, of the rectangle.

  • A9.6525𝐴10.3525cmcm
  • B9.31𝐴<10.71cmcm
  • C9.31𝐴10.71cmcm
  • D9.6525<𝐴10.3525cmcm
  • E9.6525𝐴<10.3525cmcm

Q5:

A rectangle has a length of 12.4 cm and a width of 3.2 cm. Both are measured accurate to the nearest 1 decimal place. What are the upper and lower bounds that represent the perimeter of the rectangle?

  • ALowerboundcm=31.4, upperboundcm=31
  • BLowerboundcm=38.9025, upperboundcm=40.4625
  • CLowerboundcm=30.8, upperboundcm=31.6
  • DLowerboundcm=31, upperboundcm=31.4
  • ELowerboundcm=40.4625, upperboundcm=38.9025

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