Early Access

Complements to Powers of Tenदस की घात का पूरक

Find how far a number is from 100 or 1000 using exact complement arithmetic.

Popularised in modern Vedic Mathematics teaching as complements of numbers from powers of ten; mathematically complement = base − n. Always verify with ordinary subtraction. This lab locks bases 100 and 1000 only.

Recognition signal

You need the distance from a positive integer n to base 100 or 1000, where 1 ≤ n < base. The answer is the exact complement base − n.

When to use

  • You need the exact complement of n to 100 or 1000.
  • You want a fast mental path and will verify with ordinary subtraction (or n + answer = base).

When not to use

  • The base is not 100 or 1000 (for example base 10, 50, 200, or 10000 are outside the current supported range).
  • The operand is outside 1 ≤ n < base (including n ≥ base).
  • You need a non-integer or approximate complement.

Ordinary method

Subtract the operand from the base: complement = base − n. Check that n + complement = base.

Rapid method

  1. Confirm the base is 100 or 1000 and that 1 ≤ n < base.
  2. For teaching: subtract non-final digits from 9 and the final digit from 10.
  3. If n ends in zero, treat digitwise notes carefully — the algebraic result base − n remains the source of truth.
  4. Assemble the complement and verify with ordinary subtraction.

Identity: complement = base − n · check n + complement = base

Identity: complement equals base minus n; verification: n plus complement equals base

Guided examples

Complement of 64 to 100
  1. Base is 100; operand n = 64 satisfies 1 ≤ n < 100.
  2. Digit 6: subtract from 9 → 3.
  3. Final digit 4: subtract from 10 → 6.
  4. Assemble the rapid digit result and confirm it equals 36.
  5. Ordinary check: 100 − 64 = 36.
  6. Verification: 64 + 36 = 100.

Ordinary verification: Ordinary: 100 − 64 = 36. Check: 64 + 36 = 100.

Complement of 357 to 1000
  1. Base is 1000; operand n = 357 satisfies 1 ≤ n < 1000.
  2. Digit 3: subtract from 9 → 6.
  3. Digit 5: subtract from 9 → 4.
  4. Final digit 7: subtract from 10 → 3.
  5. Assemble the rapid digit result and confirm it equals 643.
  6. Ordinary check: 1000 − 357 = 643.
  7. Verification: 357 + 643 = 1000.

Ordinary verification: Ordinary: 1000 − 357 = 643. Check: 357 + 643 = 1000.

Complement of 430 to 1000 (zero-ending operand)
  1. Base is 1000; operand n = 430 satisfies 1 ≤ n < 1000.
  2. Operand 430 contains a zero digit when written as 430.
  3. Do not trust a careless “all digits from 9 / final from 10” layout — a units contribution of 10 is not a single digit.
  4. Use the algebraic source of truth: complement = 1000 − 430 = 570.
  5. Ordinary check: 1000 − 430 = 570.
  6. Verification: 430 + 570 = 1000.

Ordinary verification: Ordinary truth: 1000 − 430 = 570. Zero-ending operands can confuse a careless digitwise layout; always trust base − n. Check: 430 + 570 = 1000.

When the rapid rule does not apply

Complement of 125 to 100

125 is not strictly less than base 100, so 1 ≤ n < base fails. This lab does not accept operands outside that range for complement practice.

Complement of 37 to 50

Base 50 is outside the current supported bases (only 100 and 1000). Do not apply this T02 lesson to arbitrary bases.

Common errors

  • Error reference T02-ERR-WRONG-BASE.

    Using a base outside the locked set (100 / 1000), such as 50 or 10000.

  • Error reference T02-ERR-RANGE.

    Accepting an operand with n ≥ base or n < 1.

  • Error reference T02-ERR-ZERO-ENDING.

    Trusting a digitwise layout that breaks on zero endings without checking base − n.

  • Error reference T02-ERR-DIGITWISE-ONLY.

    Skipping ordinary verification after a rapid digit rearrange.

Verification

Always check that base − n equals your answer and that n + answer = base.

Direct practice

12 exact-integer questions in fixed order. Accuracy only; no timer.

Start direct practice

Basic progress summary

Loading progress…

← Math Speed Lab