Reading and writing large numbers

When a cricket commentator says "this stadium holds one lakh and twenty thousand people", do you know exactly how to write that down? Let us learn the trick.

Idea

Numbers grow ten times bigger every time we move one digit to the left. So a $3$-digit number ($\text{hundreds}$) becomes a $4$-digit number ($\text{thousands}$), then $5$-digit ($\text{ten thousands}$), then $6$-digit ($\text{lakhs}$), then $7$-digit ($\text{ten lakhs}$), then $8$-digit ($\text{crores}$), and so on.

In the Indian system, we group digits as $\text{C, TL LL, TTh Th, H T O}$. Commas come after the hundreds, then every two digits to the left. So $12345678$ becomes $1{,}23{,}45{,}678$ and we read it as one crore, twenty-three lakh, forty-five thousand, six hundred seventy-eight.

In the international system, digits are grouped in threes. The same number $12345678$ becomes $12{,}345{,}678$ and is read as twelve million, three hundred forty-five thousand, six hundred seventy-eight.

To switch between the two, remember:

• $1$ million $= 10$ lakh.
• $1$ crore $= 10$ million.
• $1$ billion $= 100$ crore.

When you read a long number, always place the commas first. Without commas, even an adult can mis-read. With commas, you can name the leftmost group and walk to the right.

Worked examples

Example 1. Write $4053217$ in the Indian system with commas and read it aloud.

Step 1. Count the digits: $4053217$ has $7$ digits, so the leftmost group is in the ten-lakh column.

Step 2. Place commas: start from the right, put a comma after $3$ digits, then every $2$ digits , $40{,}53{,}217$.

Step 3. Read it: forty lakh, fifty-three thousand, two hundred seventeen.

Example 2. Write one crore twenty-five lakh as a numeral in both systems.

In the Indian system: one crore is $1{,}00{,}00{,}000$ and twenty-five lakh is $25{,}00{,}000$. Adding: $1{,}00{,}00{,}000 + 25{,}00{,}000 = 1{,}25{,}00{,}000.$ In the international system this is $12{,}500{,}000$, i.e., $12.5$ million.

Example 3. A city's population is $87{,}45{,}300$. Convert to the international system.

In the Indian system this reads "eighty-seven lakh forty-five thousand three hundred". In the international system, $87{,}45{,}300 = 8{,}745{,}300$, i.e., eight million, seven hundred forty-five thousand, three hundred.

Example 4. Write $9 \times 10^7$ in words (Indian and international).

$9 \times 10^7 = 9{,}00{,}00{,}000 = 90{,}000{,}000$. In Indian: nine crore. In international: ninety million.

Try it yourself

1. Place commas in $76543210$ in the Indian system and the international system.
2. Write three crore six lakh as a numeral.
3. Write $50{,}00{,}000$ in million.
4. Read aloud: $2{,}07{,}48{,}009$.
5. Convert $4.5$ million into lakhs.
6. The distance from Mumbai to Sydney is about $1{,}02{,}00{,}000$ metres. Convert to kilometres.
7. Write $7 \times 10^6$ in the Indian system with commas.
8. Which is larger, $9$ lakh or $1$ million? By how much?

Activity

Collect five large numbers from today's newspaper or the back of a packaged product. For each, write it both in the Indian and the international system. Underline which form makes it easier to "feel" the size.

Make flashcards: one side shows a numeral with commas, the other side shows the words. Mix and quiz a friend.