Converting to and from standard form

Converting to and from standard form

Converting to and from standard form

Scientific notation and the ordinary (standard) form are two ways to write the same number. You should be able to move between them in both directions.

From scientific notation to standard form

Multiplying by 10ⁿ moves the decimal point n places to the right. For 3.4 × 10⁴:

start with 3.4, move the point 4 places right → 34 000. Fill the empty places with zeros.

From standard form to scientific notation

Put the decimal point just after the first non-zero digit so the coefficient is between 1 and 10, then count how many places it moved — that count is the exponent. For 52 000 the coefficient is 5.2 and the point moved 4 places, so 52 000 = 5.2 × 10⁴.

A common mistake

Writing 34 × 10³ is not proper scientific notation, because 34 is not between 1 and 10. Always check 1 ≤ a < 10.

Three rules that always help

  • To expand, move the point right by the exponent and add zeros.
  • To write in scientific notation, place the point after the first digit and count the shift.
  • The coefficient must stay between 1 and 10.

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