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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`

Numbers of Any Magnitude, SMB-023

A red blood cell and a white blood cell have a combined total mass of `4.2 xx 10^-11` grams.

If the red blood cell has a mass of `2 xx 10^-12` grams, what is the mass of the white blood cell?  (2 marks)

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`4.0 xx 10^-11\ text(grams)`

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`text{Mass}` `=4.2 xx 10^-11-2 xx 10^-12`  
  `= 4.0 xx 10^-11\ text{(by calculator)}`  

Numbers of Any Magnitude, SMB-021

An insect expert estimates that an anthill 30 cm high contains `10^8` ants.

He also estimates that a 25 cm high anthill contains `10^7` ants.

If his estimations are correct, how many more ants live in the 30 cm high anthill than the 25 cm high one?  (2 marks)

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`text(90 million)`

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`text(The extra ants in the 30 cm high anthill)`

`= 100\ 000\ 000-10\ 000\ 000`

`=90\ 000\ 000`

`=90\ text(million)`

Numbers of Any Magnitude, SMB-015

The width of red blood cell is 8 nanometres or `8 xx 10^{-9}` metres.

How many red blood cells, lined up side by side in straight line, would it take to form a 1 cm distance.  (2 marks)

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`1.25 xx 10^6`

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`text{Convert cm to metres:}`

`text{100 cm = 1 m}\ => \ text{1 cm = 0.01 m}`

`text{Number of cells}` `=0.01/(8xx10^{-9})`  
  `=1\ 250\ 000`  
  `=1.25 xx 10^6`  

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 scientific notation, 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)`

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`