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Measurement, STD1 M1 2025 HSC 4 MC

What is \(6\ 280\ 000\) in standard form?

  1. \(628\times 10^4\)
  2. \(62.8\times 10^5\)
  3. \(6.28\times 10^6\)
  4. \(0.628\times 10^7\)
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\(C\)

Show Worked Solution

\(6\ 280\ 000=6.28\times 10^6\)

\(\Rightarrow C\)

Filed Under: Identify and Convert Between Units (Std2-2027), Units and Measurement Error (Std 1) Tagged With: Band 3, smc-1120-20-Scientific Notation, smc-6303-40-Scientific Notation

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`

Show Worked Solution

♦ 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`

Filed Under: Units and Measurement Error (Std2-X) Tagged With: Band 5, smc-1120-20-Scientific Notation, smc-1120-30-Significant Figures, smc-797-20-Scientific Notation, smc-797-30-Significant Figures

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}`
Show Answers Only

`C`

Show Worked Solution

`384\ 400`

`= 3.844 × 10^5`

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

 
`⇒ C`

Filed Under: Units and Measurement Error (Std2-X) Tagged With: Band 5, num-title-ct-corea, num-title-qs-hsc, smc-1120-20-Scientific Notation, smc-1120-30-Significant Figures, smc-4232-30-Scientific notation, smc-4232-50-Significant figures, smc-797-20-Scientific Notation, smc-797-30-Significant Figures

Measurement, STD1 M1 2022 HSC 1 MC

What is 650 000 000 expressed in standard form?

  1. `6.5 xx10^(7)`
  2. `6.5 xx10^(8)`
  3. `65 xx10^(6)`
  4. `65 xx10^(7)`
Show Answers Only

`B`

Show Worked Solution

`650\ 000\ 000 = 6.5 xx 10^8`

`=>B`


♦ Mean mark 45%.

Filed Under: Identify and Convert Between Units (Std2-2027), Units and Measurement Error (Std 1) Tagged With: Band 5, smc-1120-20-Scientific Notation, smc-6303-40-Scientific Notation

Measurement, STD1 M1 2020 HSC 3 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)`
Show Answers Only

`B`

Show Worked Solution

♦♦♦ Mean mark 12%.
`0.002073` `= 2.073 xx 10^(-3)`  
  `=2.1 xx 10^(-3)\ \ \ text{(to 2 sig fig)}`  

 
`=> B`

Filed Under: Units and Measurement Error (Std 1) Tagged With: Band 6, smc-1120-20-Scientific Notation, smc-1120-30-Significant Figures

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)`
Show Answers Only

`D`

Show Worked Solution

♦♦ 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`

Filed Under: Identify and Convert Between Units (Std2-2027), Units and Measurement Error (Std 1), Units and Measurement Error (Std 2) Tagged With: Band 5, smc-1120-20-Scientific Notation, smc-1120-30-Significant Figures, smc-6303-40-Scientific Notation, smc-6303-50-Significant Figures, smc-797-20-Scientific Notation, smc-797-30-Significant Figures

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)`
Show Answers Only

`D`

Show Worked Solution

♦♦ 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`

Filed Under: Identify and Convert Between Units (Std2-2027), MM1 - Units of Measurement, Numbers of Any Magnitude, Units and Measurement Error (Std 1), Units and Measurement Error (Std 2) Tagged With: Band 5, num-title-ct-corea, num-title-qs-hsc, smc-1120-20-Scientific Notation, smc-1120-30-Significant Figures, smc-4232-30-Scientific notation, smc-4232-50-Significant figures, smc-6303-40-Scientific Notation, smc-6303-50-Significant Figures, smc-797-20-Scientific Notation, smc-797-30-Significant Figures

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)`
Show Answers Only

`B`

Show Worked Solution

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

`= 3.26 xx 10^-7\ \ text(mm)`

`=> B`

Filed Under: Identify and Convert Between Units (Std2-2027), MM1 - Units of Measurement, Units and Measurement Error (Std 1), Units and Measurement Error (Std 2) Tagged With: Band 3, smc-1120-20-Scientific Notation, smc-6303-40-Scientific Notation, smc-797-20-Scientific Notation

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)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

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

Show Worked Solution
♦♦♦ 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)`

Filed Under: Identify and Convert Between Units (Std2-2027), MM1 - Units of Measurement, Units and Measurement Error (Std 1), Units and Measurement Error (Std 2) Tagged With: Band 6, smc-1120-20-Scientific Notation, smc-6303-30-Capacity/Volume/Mass, smc-6303-40-Scientific Notation, smc-797-20-Scientific Notation

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