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1Place Value to Billions2Roman Numeral Arithmetic3Twin Primes & Co-primes4Divisibility Rules5Cryptarithm Puzzles6Estimation of Products7Division Cryptarithms

Concept 1 of 7

Place Value to Billions

1

Today's big idea

International grouping runs in threes all the way, adding a new name every three digits.

One billion is a hundred crore, so the two systems step at different sizes.

2

How it works

👀 What's going on?

A headline says a company is worth nine billion, and the number has more digits than your place value house has rooms. The house does not change though. It just gets one more wing.

💡 Here's the trick

Place value to billions8B2HM3TM7M5HTh0TTh6Th9H1T4O8,237,506,914 = 8 billion 237 million 506 thousand 9147 sits at millions placePlace value = 7,000,000 = 7 millions1 million = 10 lakh · 1 crore = 10 million · 1 billion = 100 croreComma every 3 digits from the right (International system)

Look at the chart above. International grouping runs in threes the whole way: ones, then thousands, then millions, then billions. Each new group adds exactly three digits and nothing else moves.

🪄 How to do it

  1. 1.Mark the number above into groups of three, counting from the right.
  2. 2.Name the groups outwards: thousands, millions, billions.
  3. 3.Read the digit you want against the group it sits in.

✍️ Try it

In 6,704,235,918, what is the place value of the 7? Then: how many millions make one billion?

The groups are 6 | 704 | 235 | 918, so the 7 is the hundred-millions digit, worth 700,000,000. One billion is 1,000 million.

⚠️ Watch out

You might be thinking a billion is the next step up from a crore. It is not. One crore is ten million, and one billion is a hundred crore, so the two systems step at different sizes.

🌟 Why this matters

Populations, national budgets and distances between planets all live at this size, and reports quote them in millions and billions.
Exam tip: Put the commas in first, because the groups then name themselves.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“What is the place value of the 4 in 2,436,000,000?”

  1. 1

    Count from the right

    The 4 is the 9th digit from the right.

  2. 2

    Identify the place

    9th from right = HUNDRED-MILLIONS place.

  3. 3

    Multiply

    4 × 100,000,000 = 400,000,000.

  4. 4

    Answer ✓

    4 hundred millions

Now you try one — same steps, different story 👇

4

See it in action

⚡ Time to play!

Place value = the digit × the value of its column (ones, tens, hundreds, thousands, …).

PLACE VALUE · ROUND 1 OF 3

3,481,027

What is the place value of the digit 4?

5

Quick check

✅ VERIFICATION

How many zeros follow the 1 in one billion?

⚡ Finish the activity above first to answer.

Keep going!

Up next: Roman Numeral Arithmetic

Romans are easy if you visit Arabic-land in the middle.

Concept 2 of 7 →