Answered

  1. In 1920, the population of the world was 1.8 billion. By 2000, the world's population was 6 billion. Find the increase in world population during those 80 years.


  1. In 2007, the population of Nigeria was 140 million. By 2012, the population was 170.1 million.
AWhat was the increase in Nigeria's population during these 5 years?
BExpress the increase in standard form to 1 significant figure.


  1. The area of Liberia is approximately 10 times the area of The Gambia. If the area of The Gambia is approximately 1.1 × 10^4 km², find the approximate area of Liberia.


  1. The distance between two points is 2.54 × 10^-2 m. Express this distance in km in standard form.


  1. The pages of a book are numbered 1 to 300.
AHow many thicknesses of paper make 300 pages?
BIf the thickness of the book is 15 mm, calculate the thickness of 1 leaf. Give your answer in metres in standard form.

Verified Answer :

  • Difference in mountain heights: \(\boxed{2960\text{ m}}\).
  • Global population increase: \(\boxed{4.2\text{ billion}}\).
  • Nigeria population increase (a): \(\boxed{30.1\text{ million}}\), (b) standard form: \(\boxed{3 \times 10^7}\).
  • Liberia area: \(\boxed{110000\text{ km}^2}\); Distance in km: \(\boxed{2.54 \times 10^{-5}\text{ km}}\); Leaf count: \(\boxed{150}\); Leaf thickness: \(\boxed{1 \times 10^{-4}\text{ m}}\).

Explanation

  1. Step-by-Step Problem Resolution
  2. Mount Everest's height is \(8.85 \times 10^3\) m, which equals 8850 m. Mount Kilimanjaro's height is \(5.89 \times 10^3\) m, which equals 5890 m. The difference is \(8850 - 5890 = \boxed{2960\text{ m}}\).
  3. The population increased from 1.8 billion to 6 billion. The increase is \(6 - 1.8 = \boxed{4.2\text{ billion}}\).
  4. Nigeria's population grew from 140 million to 170.1 million. (a) The increase is \(170.1 - 140 = \boxed{30.1\text{ million}}\). (b) Expressing 30.1 million (\(30.1 \times 10^6 = 3.01 \times 10^7\)) in standard form to 1 significant figure gives \(\boxed{3 \times 10^7}\).
  5. The area of The Gambia is \(1.1 \times 10^4\text{ km}^2\). The area of Liberia is 10 times that: \(10 \times (1.1 \times 10^4) = 1.1 \times 10^5 = \boxed{110000\text{ km}^2}\).
  6. A distance of \(2.54 \times 10^{-2}\text{ m}\) converted to km is \(2.54 \times 10^{-2} \times 10^{-3}\text{ km} = \boxed{2.54 \times 10^{-5}\text{ km}}\).
  7. A book with 300 pages (a) has \(300 / 2 = \boxed{150}\) leaves. (b) With a total thickness of 15 mm (\(0.015\text{ m}\)), the thickness of one leaf is \(0.015 / 150 = 0.0001\text{ m}\), which in standard form is \(\boxed{1 \times 10^{-4}\text{ m}}\).

Examples

Scientific notation and unit conversion are essential in fields like geography and logistics. For instance, measuring distances on a global scale (like the distance between cities) or calculating the volume of materials for manufacturing (like paper thickness for mass printing) requires precise management of powers of ten and unit consistency. This ensures that calculations remain accurate even when numbers are extremely large or small.

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