Share such large-number facts you know / come across with your class.

Question

Homi · Accepted Answer

Understand the Question

Large numbers in mathematics and science are often expressed using powers of 10 (scientific notation) to make them easier to write and comprehend.
In exponential form, $10^n$ represents $1$ followed by $n$ zeros.
We can describe interesting and real-world large numbers by examining their exponential representations.

Step 1 · Googol

A Googol is $1$ followed by $100$ zeros:

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

Step 2 · Googolplex

A Googolplex is $1$ followed by a Googol of zeros:

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

Step 3 · Grains of Sand on Earth

The estimated number of grains of sand on all the beaches and deserts of Earth is about $7$ quintillion ( $7$ followed by $18$ zeros):

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

Step 4 · Stars in the Observable Universe

The estimated total number of stars in the observable universe is approximately:

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

Step 5 · Avogadro's Number

In chemistry, Avogadro's constant gives the number of particles (atoms or molecules) in one mole of a substance:

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

Answer

Googol: $10^{100}$

Common Mistakes

Googol vs. Googolplex: A Googol is $10^{100}$ ( $100$ zeros), whereas a Googolplex is $10^{10^{100}}$ (a Googol of zeros), which is immensely larger.
Base and Exponent Confusion: Confusing $10^{100}$ with $100^{10}$ or $10 \times 100$ . The exponent indicates the number of zeros following $1$ when the base is $10$ .

Question 3