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Measurement, STD2 EQ-Bank 06

The distance between planets is measured in Astronomical Units (AU).

\(1\ \text{AU}\ \approx 1.496\times 10^8\) kilometres.

Given Venus is approximately 0.7 AU from Earth, calculate this distance in kilometres giving your answer in scientific notation, correct to 3 significant figures.  (2 marks)

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\(1.03\times 10^8\ \text{(3 sig. fig.)}\)

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\(\text{Distance}\) \(=0.7\times \left(1.496\times 10^8\right)\)
  \(=102\,830\,000\)
  \(=1.0283\times 10^8\)
  \(=1.03\times 10^8\ \text{(3 sig. fig.)}\)

Measurement, STD2 EQ-Bank 02 MC

Arrange the numbers \(5.6\times 10^{-2}\), \(4.8\times 10^{-1}\), \(7.2\times 10^{-2}\) from smallest to largest.

  1. \(5.6\times 10^{-2}\),  \(7.2\times 10^{-2}\),  \(4.8\times 10^{-1}\)
  2. \(4.8\times 10^{-1}\),  \(5.6\times 10^{-2}\),  \(7.2\times 10^{-2}\)
  3. \(7.2\times 10^{-2}\),  \(5.6\times 10^{-2}\),  \(4.8\times 10^{-1}\)
  4. \(4.8\times 10^{-1}\),  \(7.2\times 10^{-2}\),  \(5.6\times 10^{-2}\)
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\(A\)

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\(5.6\times 10^{-2}=0.052\)

\(4.8\times 10^{-1}=0.48\)

\(7.2\times 10^{-2}=0.072\)

\(\therefore\ \text{Correct order is: }\ 5.6\times 10^{-2}\),  \(7.2\times 10^{-2}\),  \(4.8\times 10^{-1}\)

\(\Rightarrow A\)

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 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`

Measurement, STD2 M1 2007 HSC 1 MC

What is  `0.000\ 000\ 326`  mm expressed in scientific notation?

  1. `0.326 xx 10^-6\ \ text(mm)`
  2. `3.26 xx 10^-7\ \ text(mm)`
  3. `0.326 xx 10^6\ \ text(mm)`
  4. `3.26 xx 10^7\ \ text(mm)`
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`B`

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`0.000\ 000\ 326\ text(mm)`

`= 3.26 xx 10^-7\ \ text(mm)`

`=> B`

Measurement, STD2 M1 2009 HSC 25b

The mass of a sample of microbes is 50 mg. There are approximately  `2.5 × 10^6` microbes in the sample.

In standard form, what is the approximate mass in grams of one microbe?   (2 marks)

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`2 xx 10^-8\ text(grams)`

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♦♦♦ Mean mark 20%.
IMPORTANT: Can you solve: 8 apples weigh 1kg, what does 1 apple weigh? This is exactly the same concept.
`text(We need to convert 50 mg into grams)`
`50\ text(mg) = 50/1000 = 0.05\ text(g) = 5 xx 10^-2\ text(grams)`

 

`:.\ text(Mass of 1 microbe)` `= text(mass of sample)/text(# microbes)`
  `= (5 xx 10^-2)/(2.5 xx 10^6)`
  `= 2 xx 10^-8\ text(grams)`