Question

How many lakhs make a billion?

Answer 1

Hint: For this we need to understand the two types of numerical systems that is Indian and International. Since lakh is from Indian numeral system and billions are from the International system therefore we will describe both the system and show how they are written. Then we will compare the zeroes in each of the numbers and then find out the number of lakhs that are there in a billion.

Complete step by step answer:
We know that earlier there were no numbers as such and the counting was done using some kind of physical objects such as sticks or pebbles. After that lines and rock marks were used for a long time. Eventually the numbers came into existence and then there was a need to adopt a standard counting system which means a mathematical notation for expressing numbers using digits and symbols:
So we have a two numeral system one is Indian and the other one is International:
Let’s discuss Indian numeral system: So first in any given number we decide their place value which is defined as the numerical value of a digit on the basis of its position in a number. In Indian numeral system, the place values of the digits are as follows: Ones, Tens, Hundreds, Thousands, Ten Thousand, Lakhs, Ten Lakhs, Crores and so on.
Let's take an example: $13,20,12,541$
$1$ = Ones, $4$ = Tens, $5$ = Hundreds, $2$= Thousands, $1$ = Ten Thousand, $0$ = Lakhs, $2$ = Ten Lakhs, $3$ = Crores,$1$ = Ten Crores
In general we show the numbers in Indian system as follows:
One $=1$
Ten $=10$
Hundred $=100$
Thousand $=1,000$
Ten Thousand $=10,000$
One Lakh $=1,00,000$
Ten Lakh$=10,00,000$
One Crore$=1,00,00,000$
Ten Crore $=10,00,00,000$
Now let’s discuss the International Numeral system : The place values of digits go in the sequence of Ones, Tens, Hundreds, Thousands, Ten Thousand, Hundred Thousands, Millions, Ten Million and so on, in the international numeral system. Let’s take the same example again we have: $13,20,12,541$
$1$ = Ones, $4$ = Tens, $5$ = Hundreds, $2$= Thousands, $1$ = Ten Thousand, $0$ = Hundred Thousands , $2$ = Millions, $3$ = Ten Millions,$1$ = Hundred Millions
In general we display numbers in international system as follows:
One $=1$
Ten $=10$
Hundred $=100$
Thousand $=1,000$
Ten Thousand $=10,000$
Hundred Thousand $=100,000$
One Million$=1,000,000$
Ten Million$=10,000,000$
Hundred Million $=100,000,000$
One Billion = $1,000,000,000$

Now we have to find out how many lakhs are there in one billion, we have with us
One Billion = $1,000,000,000$ and One Lakh $=1,00,000$
$\begin{align}
  & \text{One Billion = }n\times \text{ One Lakh} \\
 & \Rightarrow n\text{ = }\dfrac{\text{One Billion}}{\text{One Lakh}} \\
 & \Rightarrow n\text{ = }\dfrac{\text{1,000,000,000}}{1,00,000}\Rightarrow n\text{ = 10000} \\
\end{align}$

So we see that $10000$ Lakh is there in one billion.

Note: As there are too many zeros in a billion students might get confused in dealing with them. SO keep it in mind that with the international system they place commas after three places whereas in Indian numeral system they place commas in 3,2,2... form. Such questions have very short solutions but in order to have clarity explain both the systems.