Question 3

We will explore some incredibly large numbers.

Step 1 — What is a Googol?

A Googol is a very large number.

It is 1 followed by 100 zeros.

We write it as $10^{100}$.

This number is larger than atoms in the universe.

$\boxed{1 \text{ Googol} = 10^{100}}$

Step 2 — What is a Googolplex?

A Googolplex is an even larger number.

It is 1 followed by a Googol of zeros.

We write it as $10^{\text{Googol}}$.

This number is too large to write out.

$\boxed{1 \text{ Googolplex} = 10^{\text{Googol}}}$

Step 3 — Grains of Sand

Let us estimate the number of sand grains.

Scientists estimate this number.

It is about seven quintillion.

This is 7 followed by 18 zeros.

$\boxed{7 \times 10^{18} \text{ grains}}$

Step 4 — Stars in the Universe

The universe contains many stars.

We can only see a part of it.

This is the observable universe.

It has about $10^{24}$ stars.

This is 1 followed by 24 zeros.

$\boxed{10^{24} \text{ stars}}$

Step 5 — Avogadro's Number

This number is important in chemistry.

It tells us particles in one mole.

One mole is a standard amount.

It is about $6.022 \times 10^{23}$.

This is 602,200 followed by 18 zeros.

$\boxed{6.022 \times 10^{23} \text{ particles/mole}}$

Answer

(i) A Googol is $10^{100}$, which is 1 followed by 100 zeros. (ii) A Googolplex is $10^{\text{Googol}}$, which is 1 followed by a Googol of zeros. (iii) The estimated number of sand grains on Earth is about $7 \times 10^{18}$. (iv) The estimated number of stars in the observable universe is about $10^{24}$. (v) Avogadro's Number is $6.022 \times 10^{23}$, representing particles in one mole.