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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)

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`text(0.37%)`

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`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-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)

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`1%`

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`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.

Measurement, STD2 M1 2016 HSC 1 MC

What is  208.345  correct to two significant figures?

  1. 208
  2. 210
  3. 208.34
  4. 208.35
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`B`

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`208.345 = 210\ (2\ text(sig. fig.))`

♦♦ Mean mark 36%!!

`=> B`

 

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%
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`C`

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♦ 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 2015 HSC 1 MC

What is  1 560 200 km written in standard form correct to two significant figures?

  1. `1.56 × 10^4 \ text(km)`
  2. `1.6 × 10^5 \ text(km)`
  3. `1.56 × 10^6 \ text(km)`
  4. `1.6 × 10^6 \ text(km)`
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`D`

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♦♦ Mean mark 30%.
COMMENT: Incredibly, the first MC question in 2015 had the lowest mean mark of all MC questions in the exam!

`1\ 560\ 200`

`= 1.5602 xx 10^6`

`= 1.6 xx 10^6\ text(km)\ \ \ text{(2 sig fig)}`

 
`=> D`