Question (i) to (iv) - Page 38, 39 - Getting a sense of Large Numbers - Chapter 2 Class 8 - Power Play (Ganita Prakash)

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Question (i) to (iv) - Page 38, 39 Calculate and write the answer using scientific notation: (i) How many ants are there for every human in the world?To find the number of ants for every human, you divide the total ant population by the total human population. Data from the book: The estimated global population of ants is 2 × 10^16. The global human population is about 8.2 × 10^9. Calculation: " Total Ants " /" Total Humans " =(2 × 10^16)/(8.2 × 10^9 ) =(2/8.2) × 10^(16−9) ≈0.244 × 10^7 =2.44 × 10^6 There are approximately 2.44 × 106 (or 2.44 million) ants for every human in the world Question (i) to (iv) - Page 38, 39 Calculate and write the answer using scientific notation: (ii) If a flock of starlings contains 10,000 birds, how many flocks could there be in the world?To find the number of flocks, you divide the total starling population by the number of birds in one flock. Data from the book: The estimated global population of starlings is 𝟏.𝟑 billion ( 1.3 × 10^9 ). The size of one flock is given as 10,000 (10^4 ) birds. Calculation: " Total Starlings " /" Birds per Flock " =(1.3×10^9)/10^4 =1.3 × 10^(9−4) =𝟏.𝟑 × 〖𝟏𝟎〗^𝟓 Answer: There could be 𝟏.𝟑 × 〖𝟏𝟎〗^𝟓 (or 130,000) flocks of starlings in the world. Question (i) to (iv) - Page 38, 39 Calculate and write the answer using scientific notation: (iii) If each tree had about 104 leaves, find the total number of leaves on all the trees in the world.To find the total number of leaves, you multiply the total number of trees by the average number of leaves per tree. Data from the book: The estimated number of trees globally is 𝟑 trillion ( 𝟑×〖𝟏𝟎〗^𝟏𝟐 ). The number of leaves per tree is given as about 10^4. Calculation: "Total Trees "×" Leaves per Tree "=(3×10^12 )×10^4 =3×10^(12+4) =𝟑×〖𝟏𝟎〗^𝟏𝟔 Answer: There are approximately 𝟑 × 〖𝟏𝟎〗^𝟏𝟔 leaves on all the trees in the world. Question (i) to (iv) - Page 38, 39 Calculate and write the answer using scientific notation: (iv) If you stacked sheets of paper on top of each other, how many would you need to reach the Moon?To find how many sheets of paper are needed, you divide the distance to the Moon by the thickness of a single sheet of paper. Data from the book: The distance to the Moon is 𝟑𝟖𝟒,𝟒𝟎𝟎" " 𝐤𝐦. The assumed thickness of one sheet of paper is 𝟎.𝟎𝟎𝟏" " 𝐜𝐦. Calculation: Convert units: First, make sure both measurements are in the same unit (e.g., centimeters). Distance in meters: 384,400" " km × 1000=3.844×10^8 " " m Distance in cm: (3.844×10^8 )m×100=𝟑.𝟖𝟒𝟒×〖𝟏𝟎〗^𝟏𝟎 " " 𝐜𝐦 Paper thickness: 0.001" " cm=〖𝟏𝟎〗^(−𝟑) " " 𝐜𝐦 Divide: " Distance to Moon " /" Thickness of Paper " =(3.844×10^10)/10^(−3) =3.844 × 10^(10−(−3)) =𝟑.𝟖𝟒𝟒 × 〖𝟏𝟎〗^𝟏𝟑 Answer: You would need to stack 𝟑.𝟖𝟒𝟒×〖𝟏𝟎〗^𝟏𝟑 (about 38.4 trillion) sheets of paper to reach the Moon.