smc-4232-60-Unit conversion

Numbers of Any Magnitude, SMB-017

A tennis racquet length is measured at 68.58 centimetres.

Express this measurement in metres, rounded to two decimal places. (2 marks)

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`0.69\ text{m}`

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`text{Convert cm → metres:}`

`68.58\ text{cm}\ = 68.58/100 = 0.6858\ text{m}`

`0.6858\ text{m}\ = 0.69\ text{m (to 2 d.p.)}`

Numbers of Any Magnitude, SMB-016

A solution of acid is measures 12 982 millilitres.

Express this measurement in litres, correct to one decimal place. (2 marks)

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`13.0\ text{litres}`

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`text{12 982 mL}\ =(12\ 982)/1000 = 12.982\ text{litres}`

`12.982\ text{L}\ = 13.0\ text{L (to 1 d.p.)}`

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)

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

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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)`

Numbers of Any Magnitude, SMB-008 MC

A person's height is measured as 1.7 metres.

What is the absolute error of this measurement?

1 centimetre
5 centimetres
10 centimetres
50 centimetres

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`B`

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`text{1 metre = 100 cm}\ => \ text{0.1 metre = 10 cm}`

`text(A)text(bsolute error)`	`= 1/2 xx\ text(precision)`
	`= 1/2 xx 0.1\ text(m)`
	`= 1/2 xx 10\ text(cm)`
	`= 5\ text(cm)`

`=> B`

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 2019 HSC 8 MC

A person's weight is measured as 79.3 kg.

What is the absolute error of this measurement?

10 grams
50 grams
100 grams
500 grams

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`B`

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♦ Mean mark 46%.

`text(A)text(bsolute error)`	`= 1/2 xx\ text(precision)`
	`= 1/2 xx 0.1\ text(kg)`
	`= 1/2 xx 100\ text(grams)`
	`= 50\ text(grams)`

`=> B`