Question 16

We will use scientific notation to express very large numbers in a compact way. Scientific notation writes a number as a product of a number between 1 and 10 and a power of 10.

Step 1 — Total clothing pieces

Let us find the total number of clothes. We multiply the world population by clothes per person. The world population is about $8 \times 10^9$ people. Each person has 30 pieces of clothing.

$\text{Total clothes} = (\text{World population}) \times (\text{Clothes per person})$

$= (8 \times 10^9) \times 30$

$= (8 \times 30) \times 10^9$

$= 240 \times 10^9$

To write this in scientific notation, we change 240 to $2.4 \times 10^2$.

$= (2.4 \times 10^2) \times 10^9$

$= 2.4 \times 10^{(2+9)}$

$\boxed{2.4 \times 10^{11} \text{ pieces of clothing}}$

Step 2 — Total honeybees

We need to find the total number of honeybees. We multiply the number of bee colonies by bees per colony. There are 100 million bee colonies. One million is $10^6$. So, 100 million is $100 \times 10^6 = 10^2 \times 10^6 = 10^8$. Each colony has 50,000 bees. 50,000 is $5 \times 10^4$.

$\text{Total bees} = (\text{Number of colonies}) \times (\text{Bees per colony})$

$= (1 \times 10^8) \times (5 \times 10^4)$

$= (1 \times 5) \times (10^8 \times 10^4)$

$= 5 \times 10^{(8+4)}$

$\boxed{5 \times 10^{12} \text{ bees}}$

Step 3 — Total bacterial population

Let us calculate the total bacterial cells. We multiply the world population by bacterial cells per human. The world population is $8 \times 10^9$. Each human body has 38 trillion bacterial cells. One trillion is $10^{12}$. So, 38 trillion is $38 \times 10^{12}$. We write $38$ as $3.8 \times 10^1$. So, $3.8 \times 10^1 \times 10^{12} = 3.8 \times 10^{13}$.

$\text{Total bacteria} = (\text{World population}) \times (\text{Bacterial cells per human})$

$= (8 \times 10^9) \times (3.8 \times 10^{13})$

$= (8 \times 3.8) \times (10^9 \times 10^{13})$

$= 30.4 \times 10^{(9+13)}$

$= 30.4 \times 10^{22}$

To write this in scientific notation, we change 30.4 to $3.04 \times 10^1$.

$= (3.04 \times 10^1) \times 10^{22}$

$= 3.04 \times 10^{(1+22)}$

$\boxed{3.04 \times 10^{23} \text{ bacterial cells}}$

Step 4 — Total eating time in a lifetime

We need to find the total time spent eating in seconds. First, we convert daily eating time to seconds. Average eating time per day is 1.5 hours. There are 60 minutes in an hour and 60 seconds in a minute.

$\text{Eating time per day in seconds} = 1.5 \text{ hours} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute}$

$= 1.5 \times 3600$

$= 5400 \text{ seconds}$

Next, we find the number of days in an average lifespan. Average lifespan is 70 years. There are 365 days in a year.

$\text{Number of days in lifespan} = 70 \text{ years} \times 365 \text{ days/year}$

$= 25550 \text{ days}$

Finally, we multiply daily eating time by the number of days in a lifespan.

$\text{Total eating time in lifespan} = (\text{Eating time per day}) \times (\text{Number of days in lifespan})$

$= 5400 \times 25550$

$= 137,970,000 \text{ seconds}$

To write this in scientific notation, we move the decimal point 8 places to the left.

$\boxed{1.3797 \times 10^8 \text{ seconds}}$

Answer

(i) The total number of pieces of clothing is $2.4 \times 10^{11}$. (ii) The total number of honeybees is $5 \times 10^{12}$. (iii) The total bacterial population residing in all humans is $3.04 \times 10^{23}$. (iv) The total time spent eating in a lifetime is $1.3797 \times 10^8$ seconds.