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Numbers of Any Magnitude, SMB-008 MC

A person's height is measured as 1.7 metres.

What is the absolute error of this measurement?

  1. 1 centimetre
  2. 5 centimetres
  3. 10 centimetres
  4. 50 centimetres
Show Answers Only

`B`

Show Worked Solution

`text{1 metre = 100 cm}\ => \ text{0.1 metre = 10 cm}`

`text(A)text(bsolute error)` `= 1/2 xx\ text(precision)`
  `= 1/2 xx 0.1\ text(m)`
  `= 1/2 xx 10\ text(cm)`
  `= 5\ text(cm)`

 
`=> B`

Numbers of Any Magnitude, SMB-007

The capacity of a bottle is measured as 1.35 litres correct to the nearest 10 millilitres.

What is the percentage error for this measurement, correct to two significant figures?   (2 marks)

Show Answers Only

`text(0.37%)`

Show Worked Solution

`text{1.35 litres = 1350 milliliters (mL)}`

`text(A) text(bsolute error) = 1/2 xx\ text{precision} = 1/2xx10=5\ text(mL)`

`:.\ text(% error)` `= 5/1350 xx 100`
  `=0.3703… %`
  `=0.37%\ text{(to 2 sig.fig.)}`

Numbers of Any Magnitude, SMB-006

A dinosaur fossil is measured to be 1.3 metres in length.

What is the percentage error in this measurement, giving your answer correct to two decimal places?  (2 marks)

Show Answers Only

`3.85%`

Show Worked Solution

`text{Absolute error} = 1/2 xx \text{precision} = 1/2 xx 0.1 = 0.05\ text{m}`

`%  text(error)` `= frac(0.05)(1.3) xx 100`
  `= 3.84615%`
  `=3.85%\ text{(to 2 d.p.)}`

Numbers of Any Magnitude, SMB-005

A puppy's weight is measured at 5.2 kilograms, to the nearest 100 grams.

Calculate the percentage error in this measurement, correct to one significant figure?  (3 marks)

Show Answers Only

`1%`

Show Worked Solution

`text{Using  1 kilogram = 1000 grams}`

`=>\ text{5.2 kilograms = 5200 grams}`

`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 100 = 50\ text{g}`

`text{% error}` `=\ frac{text{absolute error}}{text{measurement}} xx 100%`  
  `=50/5200 xx 100%`  
  `=0.961… %`  
  `=1%\ text{(to 1 sig. fig.)}`  
TIP: Convert all measurements to either grams or kilograms before applying formula.

Numbers of Any Magnitude, SMB-004

The height of palm tree is measured at 8 metres, to the nearest metre.

What is the percentage error in this measurement?  (2 marks)

Show Answers Only

`6.25%`

Show Worked Solution

`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 1 = 0.5\ text{m}`

`text{% error}` `=\ frac{text{absolute error}}{text{measurement}} xx 100%`  
  `=0.5/8 xx 100%`  
  `=6.25%`  

Numbers of Any Magnitude, SMB-003

The width of a hockey field is measured to be 45 metres, correct to the nearest metre.

What is the upper limit for the width of the hockey field?  (2 marks)

Show Answers Only

`45.5\ text(m)`

Show Worked Solution

`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 1 = 0.5\ text{m}`

`=>\ text{True length could lie 0.5 metres either side of 45 m measurement.}`

`:.\ text(Upper limit)` `= 45+0.5`
  `= 45.5\ text(m)`

Numbers of Any Magnitude, SMB-002 MC

The width of a soccer field is measured to be 50.60 metres, correct to the nearest centimetre.

What is the lower limit for the length of the netball court?

  1. 50.55 m
  2. 50.59 m
  3. 50.595 m
  4. 50.599 m
Show Answers Only

`C`

Show Worked Solution

`text{1 cm = 0.01 metre}`

`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 0.01 = 0.005\ text{m}`

`:.\ text(Lower limit)` `= 50.60-0.005`
  `= 50.595\ text(m)`

 
`=>C`

Numbers of Any Magnitude, SMB-001

A cockroach is measured in a school science experiment and its length is recorded as 5.2 cm.

What is the upper limit of accuracy of this measurement?  (2 marks)

Show Answers Only

`5.25\ text(cm)`

Show Worked Solution

`text{Absolute error} = 1/2 xx \text{precision} = 1/2 xx 0.1 = 0.05\ text{cm}`

`=>\ text{True length could lie 0.05 cm either side of 5.2 cm measurement.}`

`text(Upper limit)` `= 5.2 + 0.05`
  `= 5.25\ text(cm)`

Measurement, STD2 M1 2020 HSC 5 MC

A plant stem is measured to be 16.0 cm, correct to one decimal place.

What is the percentage error in this measurement?

  1.  0.3125%
  2.  0.625%
  3.  3.125%
  4.  6.25%
Show Answers Only

`A`

Show Worked Solution

♦ Mean mark 41%.

`text{Absolute error} = 1/2 xx \text{precision} = 1/2 xx 0.1 = 0.05\ text{cm}`

`%  text(error)` `= frac(0.05)(16.0) xx 100`
  `= 0.3125%`

 
`=> \ A`

Measurement, STD2 M1 2019 HSC 8 MC

A person's weight is measured as 79.3 kg.

What is the absolute error of this measurement?

  1. 10 grams
  2. 50 grams
  3. 100 grams
  4. 500 grams
Show Answers Only

`B`

Show Worked Solution

♦ Mean mark 46%.

`text(A)text(bsolute error)` `= 1/2 xx\ text(precision)`
  `= 1/2 xx 0.1\ text(kg)`
  `= 1/2 xx 100\ text(grams)`
  `= 50\ text(grams)`

 
`=> B`

Measurement, STD2 M1 2018 HSC 18 MC

The length of a window is measured as 2.4 m.

Which calculation will give the percentage error for this measurement?

  1. `0.05/2.4 xx 100`
  2. `0.05/100 xx 2.4`
  3. `0.5/2.4 xx 100`
  4. `0.5/100 xx 2.4`
Show Answers Only

`A`

Show Worked Solution

`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 0.1 = 0.05\ text{m}`

`text{% error}` `=\ frac{text{absolute error}}{text{measurement}} xx 100%`  
  `=0.05/2.4 xx 100%`  

 
`=>A`

Measurement, STD2 M1 2015 HSC 12 MC

The length of a fish was measured to be 49 cm, correct to the nearest cm.

What is the percentage error in this measurement, correct to one significant figure?

  1. 0.01%
  2. 0.5%
  3. 1%
  4. 2%
Show Answers Only

`C`

Show Worked Solution
♦ Mean mark 41%.

`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 1 = 0.5\ text{cm}`

`text{% error}` `=\ frac{text{absolute error}}{text{measurement}} xx 100%`  
  `=0.5/49 xx 100%`  
  `=1.020… %`  
  `=1%\ \ text{(to 1 sig fig)}`  

 
`=>C`

Measurement, STD2 M1 2014 HSC 10 MC

The top of the Sydney Harbour Bridge is measured to be 138.4 m above sea level. 

What is the percentage error in this measurement?

  1. 0.036%
  2. 0.050%
  3. 0.072%
  4. 0.289%
Show Answers Only

`A`

Show Worked Solution
 
♦ Mean mark 48%

`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 0.1 = 0.05\ text{m}`

`text{% error}` `=\ frac{text{absolute error}}{text{measurement}} xx 100%`  
  `=0.05/138.4 xx 100%`  
  `=0.036%`  

 
`=>  A`

Measurement, STD2 M1 2013 HSC 27d

A rectangular wooden chopping board is advertised as being 17 cm by 25 cm, with each side measured to the nearest centimetre.

  1. Calculate the percentage error in the measurement of the longer side.   (1 mark)

  2. Between what lower and upper limits does the actual area of the top of the chopping board lie?     (2 marks)

Show Answers Only
  1. `text(2%)`
  2. `404.25\ text{cm}^2 and 446.25\ text{cm}^2`
Show Worked Solution

i.    `text(Longer side) = 25\ text(cm)`

♦♦ Mean mark 23%
MARKER’S COMMENT: Be aware that measurements accurate to the nearest cm have an absolute error for calculation purposes of 0.5 cm.

`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 1 = 0.5\ text{cm}`

`text{% error}` `=\ frac{text{absolute error}}{text{measurement}} xx 100%`  
  `=0.5/25 xx 100%`  
  `=2%`  

 

ii.   `text(Area) = l xx b`

♦ Mean mark 35%
`text{Area (upper)}` `=25.5 xx 17.5`
  `=446.25\ text{cm}^2`

 

`text{Area (lower)}` `=24.5 xx 16.5`
  `=404.25\ text{cm}^2`

 
`:.\ text{Area is between 404.25 cm}^2\ text{and 446.25 cm}^2.`