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Place value

What is the 7 in 3,472,105 worth? Round it to the nearest thousand. Write 34,72,105 the international way; 45 lakh in millions. Digits without end.

  • Number sense
  • Timed
  • Endless levels

How it plays

Four kinds of question: the value of one digit in a long number; the number rounded to a place; the same number with international commas (3,472,105) or Indian ones (34,72,105); and an amount in lakh or crore given in million or billion, or the other way.

One lakh is 100,000 — a tenth of a million — and one crore is 10 million; 100 crore is a billion. The usual slip is a factor of ten, and it is always among the options.

Levels add a digit without end, bring in billion, trillion and lakh crore, and shorten the time. The working names the place, or the factor.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

This trains reading and converting large numbers. It is practice at this, nothing wider.

Learn

How to get better at place value: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. Look at the commas before the digits. Groups of three throughout means international (3,472,105); three at the end and pairs before it means Indian (34,72,105).
  2. Find your place by its comma group, not by counting single digits from the left: the group tells you thousands, lakhs, millions or crores at once.
  3. Answer in the same grouping you were asked in, unless the question asks you to change it.
  4. Before you choose, check the size of your answer against the question. Most wrong options are a power of ten out, so they carry a zero too many or too few.

Techniques and tricks

  • Name the comma groups

    International: the last group is units, then thousands, millions, billions. Indian: the last three are units, then pairs for thousands, lakhs and crores. A digit’s value is its place in its group times that group’s name.

    e.g. The 7 in 3,472,105 sits in the thousands group, 472, as its tens digit: 7 × 10 thousand = 70,000

  • Read Indian numbers aloud

    Say each group with its name, left to right. Saying it is how the size sticks.

    e.g. 34,72,105 is “34 lakh, 72 thousand, 105”; 4,25,00,000 is “4 crore 25 lakh”

  • Regroup from the right

    To change commas, drop them, then put new ones back from the right: every three digits for international; three, then every two, for Indian. Never move commas from the left.

    e.g. 3,472,105 → 3472105 → 105, then 72, then 34 → 34,72,105

  • Scales as powers of ten

    Thousand is 10³, lakh 10⁵, million 10⁶, crore 10⁷, billion 10⁹; trillion and lakh crore are both 10¹². To convert, subtract the powers and shift the point that many places.

    e.g. 45 lakh in millions: 5 − 6 = −1, so one place left: 4.5 million. 3.2 billion in crore: 9 − 7 = 2, so 320 crore.

  • Four bridges to remember

    Ten lakh is a million. A crore is ten million. A hundred crore is a billion. A lakh crore is a trillion. Most conversions are one of these, with a shift.

    e.g. 250 crore = 2.5 × 100 crore = 2.5 billion

  • One digit decides the rounding

    Find the place you are rounding to and look only at the digit just to its right: 5 or more rounds up, less leaves it. Everything further right is noise.

    e.g. 3,586 to the nearest 100: the digit after the 5 is 8, so 3,600

As the levels climb

  • A digit is added every few levels, without end. Long numbers are where counting from the left fails; find the comma group first, then the place inside it.
  • Billion joins thousand, lakh, million and crore early on, then trillion and lakh crore. Learn their powers of ten — 9 and 12 — before they arrive, and the conversions stay a matter of shifting the point.
  • As the digits grow, the amounts to convert gain significant figures and sometimes a decimal place, like 4.5 lakh or 38.6 million. Shift the point the same way; the digits do not change, only where the point sits.
  • The clock closes to 62% of its starting time. With fewer seconds, rely on the digit count of the answer rather than reading every digit of every option.

Traps to avoid

  • One place out: the 5 in 9,256 answered as 500 or 5 instead of 50. Say the place out loud — “tens” — before you choose.
  • The digit at face value. The 5 is worth 5 only in the units place; everywhere else it carries zeros.
  • Rounding that truncates: 3,586 to the nearest 100 answered as 3,500, because the tail was dropped instead of looked at. Or rounding at the next place along, giving 3,590 or 4,000.
  • A regrouped number with a digit gained or lost. The Indian and international forms look so different that 3,47,21,050 can pass for 34,72,105. Count the digits: they must match.
  • A conversion a power of ten out — 45 lakh as 45 million or 0.45 million. Check with a bridge: 10 lakh is a million, so 45 lakh is a bit under 5 million.

How to practise

  • Set “Commas” to the grouping you are less used to — “Indian: 34,72,105” or “International: 3,472,105” — and stay there until you read it as fast as your own.
  • Use “Questions” to drill “Lakh and crore ↔ million and billion” on its own; it has the most to memorise — seven names and their powers of ten.
  • Switch “Answer by” to “Typing the number” once choosing is easy: then the digit count must come from you, not from the options. Very long answers are typed as digits without commas; “International ↔ Indian commas” stays a choice.
  • Raise “Options shown” to 6 or 8 to meet the ×10 and ×100 slips side by side; every one of them must be ruled out by its digit count.

Levels

Each question has a clock that comes from the work it asks for. There is no last level: at least one dial turns without end. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

More number sense

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