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v1 Measurement, STD2 M1 2020 HSC 2 MC

What is 0.0004782 expressed in standard form with two significant figures?

  1. `4.8 xx 10^(-4)`
  2. `4.78 xx 10^(-4)`
  3. `4.8 xx 10^(-5)`
  4. `4.78 xx 10^(-5)`
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`A`

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♦ Mean mark 39%.
COMMENT: Students often round incorrectly when converting to standard form.
`0.0004782` `= 4.782 xx 10^(-4)`
  `= 4.8 xx 10^(-4)\ \ \ text{(to 2 sig fig)}`

`⇒ A`

v1 Measurement, STD2 M1 2016 HSC 1 MC

What is  0.04967  correct to two significant figures?

  1. 0.049
  2. 0.050
  3. 0.0496
  4. 0.0497
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`B`

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`text(We are rounding 0.04967 to 2 significant figures.)`

• `text(First 2 significant digits: 4 and 9)`

• `text(Next digit is 6 → round **up**)`

• `text(0.04967 rounds to 0.050 (2 sig. fig.))`

`=> B`

v1 Measurement, STD2 M1 2015 HSC 1 MC

The distance from Earth to the Moon is approximately 384 400 km.

What is this distance in standard form correct to two significant figures?

  1. `3.84 × 10^5\ \text{km}`
  2. `3.8 × 10^5\ \text{km}`
  3. `3.9 × 10^5\ \text{km}`
  4. `3.84 × 10^6\ \text{km}`
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`C`

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`384\ 400`

`= 3.844 × 10^5`

`\text(Rounded to 2 significant figures)  →  3.9 × 10^5\ \text{km}`

 
`⇒ C`

Measurement, STD1 M1 2022 HSC 4 MC

The area `(A)` of a circle is given by the formula `A=\pi r^2`, where `r` is the radius.

What is the value of `A`, correct to three significant figures, if `r=3.55` ?

  1. 39.5
  2. 39.6
  3. 39.591
  4. 39.592
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`B`

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`A` `=pi\r^2`  
  `=pi xx3.55^2`  
  `=39.591…`  
  `=39.6\ \ text{(3 sig fig)}`  

  
`=>B`


♦♦ Mean mark 30%.
COMMENT: Significant figures warrant attention.

Measurement, STD2 M1 2020 HSC 2 MC

What is 0.002073 expressed in standard form with two significant figures?

  1. `2.07 xx 10^(-2)`
  2. `2.1 xx 10^(-2)`
  3. `2.07 xx 10^(-3)`
  4. `2.1 xx 10^(-3)`
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`D`

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♦♦ Mean mark 35%.
COMMENT: A notable knowledge gap flagged by this result.
`0.002073` `= 2.073 xx 10^(-3)`  
  `=2.1 xx 10^(-3)\ \ \ text{(to 2 sig fig)}`  

 
`=> D`

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 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`