What If We Have 12 Fingers?

Our number system is called the decimal system (deci means 10) because we count in groups of 10’s. This is probably because we have 10 fingers. What do I mean when I said when we count in groups of 10?

The Human Fingers

Our number system has the digits 0 to 9, and then we when we reach the 10th number, we place 1 in the tens place 0 in the ones digit. In the decimal number system, 23 means that we have 2 tens and 3 ones. Similarly, the number 452 means that we have 4 groups hundreds (10 tens), 5 groups of tens and 8 ones. In fact,  if we use the expanded notation, 452 is equal to

4 \times 10^2 + 5 \times 10^1 + 2 \times 10^0.

Notice that each number is multiplied by powers of 10. » Read more

Googol and Google

In last week’s post, we have talked about large numbers and their importance to scientific studies and everyday life. In this post, we talk about one of the most famous large numbers: googol.

A googol is the name of the number which is 10^{100} or a 1 followed by one hundred zeros. If you are wondering how large it is, well it is fairly large since the number of atoms in the observable universe is only 10^{80}. That means that we need 10^{20} universes, the size of the observable universe, to create a universe with googol number of atoms.

googol

The term googol was coined in 1938 by Milton Sirrota (he was 9 years old the time he invented the term), nephew of Edward Kasner, an American mathematician. Kasner was famous for his book Mathematics and the Imagination where he introduced the term googol. » Read more

Are all fractions rational numbers?

No.

A rational number can be expressed in the form \displaystyle\frac{a}{b} where a and b are integers and b \neq 0. In other words, it is a fraction whose denominator is not zero, and both the denominator and numerator are integers.

fractions

Some fractions, however, may contain a numerator or denominator that is not an integer. Some examples of such fractions are

\displaystyle\frac{\sqrt{3}}{2}, \displaystyle\frac{\pi}{4} and \displaystyle\frac{e}{2}.

A rational number may be represented in many ways, but it can always be expressed as a fraction. For instance, 10^{-1} is a rational number because we can express it as \frac{1}{10}. Also, the number 0.333 \cdots, a repeating decimal, is  a rational number because we can also express it as fraction \frac{1}{3}.

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