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QUESTION IMAGE

exercises: 11. re-write the following using prefix and unit symbols, an…

Question

exercises:

  1. re-write the following using prefix and unit symbols, and exponential equivalents.

(a) 2.5 centimetres
(b) 1.3 kilograms
(c) 25.2 millimoles
(d) 5.1 decigrams
(e) 0.25 megalitres
(f) 6.38 micrograms

  1. re-write the following using written prefixes and units, and exponential equivalents.

(a) 2.5 mm
(b) 6.5 dl
(c) 1.9 kmol
(d) 4 mt
(e) 9.94 cg
(f) 1.25 \\(\mu\\)s

  1. re-write the following using prefix symbols, and written prefixes and units.

(a) \\(4.5 \times 10^{-3}\\) mol
(b) \\(1.6 \times 10^{3}\\) m
(c) \\(0.50 \times 10^{-6}\\) l
(d) \\(2.68 \times 10^{-1}\\) g
(e) \\(8.85 \times 10^{6}\\) t
(f) \\(7.25 \times 10^{-2}\\) m

  1. express

(a) 50 \\(\text{cm}^3\\) in millilitres
(b) 22.5 t in kilograms
(c) 0.125 \\(\text{m}^3\\) in litres

Explanation:

Identify the objectives for each exercise

We need to solve four distinct exercises from the image:

  • Exercise 11: Convert written metric quantities into prefix and unit symbols, and their exponential equivalents (scientific notation with base units).
  • Exercise 12: Convert prefix and unit symbols into written prefixes and units, and their exponential equivalents.
  • Exercise 13: Convert exponential expressions into prefix symbols, and written prefixes and units.
  • Exercise 14: Perform specific unit conversions between metric volume and mass units.

Solve Exercise 11

We convert each written quantity into symbols and exponential equivalents:

  • (a) \(2.5\text{ centimetres}\):
  • Symbols: \(\text{cm}\)
  • Exponential: \(2.5 \times 10^{-2}\text{ m}\)
  • (b) \(1.3\text{ kilograms}\):
  • Symbols: \(\text{kg}\)
  • Exponential: \(1.3 \times 10^{3}\text{ g}\)
  • (c) \(25.2\text{ millimoles}\):
  • Symbols: \(\text{mmol}\)
  • Exponential: \(25.2 \times 10^{-3}\text{ mol}\) or \(2.52 \times 10^{-2}\text{ mol}\)
  • (d) \(5.1\text{ decigrams}\):
  • Symbols: \(\text{dg}\)
  • Exponential: \(5.1 \times 10^{-1}\text{ g}\)
  • (e) \(0.25\text{ megalitres}\):
  • Symbols: \(\text{ML}\)
  • Exponential: \(0.25 \times 10^{6}\text{ L}\) or \(2.5 \times 10^{5}\text{ L}\)
  • (f) \(6.38\text{ micrograms}\):
  • Symbols: \(\mu\text{g}\)
  • Exponential: \(6.38 \times 10^{-6}\text{ g}\)

Solve Exercise 12

We convert each symbol into written form and exponential equivalents:

  • (a) \(2.5\text{ mm}\):
  • Written: \(2.5\text{ millimetres}\)
  • Exponential: \(2.5 \times 10^{-3}\text{ m}\)
  • (b) \(6.5\text{ dL}\):
  • Written: \(6.5\text{ decilitres}\)
  • Exponential: \(6.5 \times 10^{-1}\text{ L}\)
  • (c) \(1.9\text{ kmol}\):
  • Written: \(1.9\text{ kilomoles}\)
  • Exponential: \(1.9 \times 10^{3}\text{ mol}\)
  • (d) \(4\text{ Mt}\):
  • Written: \(4\text{ megatonnes}\)
  • Exponential: \(4 \times 10^{6}\text{ t}\) (or \(4 \times 10^{9}\text{ kg}\))
  • (e) \(9.94\text{ cg}\):
  • Written: \(9.94\text{ centigrams}\)
  • Exponential: \(9.94 \times 10^{-2}\text{ g}\)
  • (f) \(1.25\ \mu\text{s}\):
  • Written: \(1.25\text{ microseconds}\)
  • Exponential: \(1.25 \times 10^{-6}\text{ s}\)

Solve Exercise 13

We convert each exponential expression into prefix symbols and written forms:

  • (a) \(4.5 \times 10^{-3}\text{ mol}\):
  • Symbols: \(4.5\text{ mmol}\)
  • Written: \(4.5\text{ millimoles}\)
  • (b) \(1.6 \times 10^{3}\text{ m}\):
  • Symbols: \(1.6\text{ km}\)
  • Written: \(1.6\text{ kilometres}\)
  • (c) \(0.50 \times 10^{-6}\text{ L}\):
  • Symbols: \(0.50\ \mu\text{L}\)
  • Written: \(0.50\text{ microlitres}\)
  • (d) \(2.68 \times 10^{-1}\text{ g}\):
  • Symbols: \(2.68\text{ dg}\)
  • Written: \(2.68\text{ decigrams}\)
  • (e) \(8.85 \times 10^{6}\text{ t}\):
  • Symbols: \(8.85\text{ Mt}\)
  • Written: \(8.85\text{ megatonnes}\)
  • (f) \(7.25 \times 10^{-2}\text{ m}\):
  • Symbols: \(7.25\text{ cm}\)
  • Written: \(7.25\text{ centimetres}\)

Solve Exercise 14

We perform the requested unit conversions:

  • (a) \(50\text{ cm}^3\) in millilitres:
  • Since \(1\text{ cm}^3 = 1\text{ mL}\), \(50\text{ cm}^3 = 50\text{ mL}\).
  • (b…

Answer:

Question 11

  • (a) Symbol: \(2.5\text{ cm}\); Exponential: \(2.5 \times 10^{-2}\text{ m}\)
  • (b) Symbol: \(1.3\text{ kg}\); Exponential: \(1.3 \times 10^{3}\text{ g}\)
  • (c) Symbol: \(25.2\text{ mmol}\); Exponential: \(25.2 \times 10^{-3}\text{ mol}\) (or \(2.52 \times 10^{-2}\text{ mol}\))
  • (d) Symbol: \(5.1\text{ dg}\); Exponential: \(5.1 \times 10^{-1}\text{ g}\)
  • (e) Symbol: \(0.25\text{ ML}\); Exponential: \(0.25 \times 10^{6}\text{ L}\) (or \(2.5 \times 10^{5}\text{ L}\))
  • (f) Symbol: \(6.38\ \mu\text{g}\); Exponential: \(6.38 \times 10^{-6}\text{ g}\)

Question 12

  • (a) Written: \(2.5\text{ millimetres}\); Exponential: \(2.5 \times 10^{-3}\text{ m}\)
  • (b) Written: \(6.5\text{ decilitres}\); Exponential: \(6.5 \times 10^{-1}\text{ L}\)
  • (c) Written: \(1.9\text{ kilomoles}\); Exponential: \(1.9 \times 10^{3}\text{ mol}\)
  • (d) Written: \(4\text{ megatonnes}\); Exponential: \(4 \times 10^{6}\text{ t}\) (or \(4 \times 10^{9}\text{ kg}\))
  • (e) Written: \(9.94\text{ centigrams}\); Exponential: \(9.94 \times 10^{-2}\text{ g}\)
  • (f) Written: \(1.25\text{ microseconds}\); Exponential: \(1.25 \times 10^{-6}\text{ s}\)

Question 13

  • (a) Symbol: \(4.5\text{ mmol}\); Written: \(4.5\text{ millimoles}\)
  • (b) Symbol: \(1.6\text{ km}\); Written: \(1.6\text{ kilometres}\)
  • (c) Symbol: \(0.50\ \mu\text{L}\); Written: \(0.50\text{ microlitres}\)
  • (d) Symbol: \(2.68\text{ dg}\); Written: \(2.68\text{ decigrams}\)
  • (e) Symbol: \(8.85\text{ Mt}\); Written: \(8.85\text{ megatonnes}\)
  • (f) Symbol: \(7.25\text{ cm}\); Written: \(7.25\text{ centimetres}\)

Question 14

  • (a) \(50\text{ mL}\)
  • (b) \(22,500\text{ kg}\) (or \(2.25 \times 10^4\text{ kg}\))
  • (c) \(125\text{ L}\)