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Scientific notation converter with steps

  

Normalised form: one non-zero digit before the decimal point.

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Scientific notation

4.52 × 10^-4

E notation: 4.52e-4

How we got this

  1. Move the decimal point until one non-zero digit is left of it: 4.52.
  2. You moved it 4 places to the right.
  3. Right moves give a negative power: × 10^-4.

Moving the decimal point

Count how many places the decimal point has to move so that one non-zero digit sits before it. That count is the power of ten: positive if the number was large, negative if it was small. To go back, move the point the other way and fill gaps with zeros.

Multiplying two numbers in this form means multiplying the coefficients and adding the powers, the exponent rule shown in the roots and exponents calculator. Roots of an equation with very large coefficients are easier to check with the quadratic solver.

Sources

What this calculator does not account for

  • Significant-figure rules for measured values.
  • Engineering notation (powers of 3).

How this is calculated

Formula: Normalised scientific notation

x =a × 10ⁿ, with 1 ≤ |a| < 10

What the symbols mean

  • aThe coefficient, one non-zero digit before the point.
  • nHow many places the decimal point moved: positive for big numbers, negative for small ones.

Good to know

  • Calculators and spreadsheets write 6.02 × 10^23 as 6.02E23.

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Worked examples

Each example is worked out by the same code as the calculator above.

Speed of light

299,792,458 m/s: move the point 8 places left: 2.99792458 × 10^8.

A cell

0.00001 m: move the point 5 places right: 1 × 10^−5.

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Questions

What is 0.000452 in scientific notation?

4.52 × 10^−4: the point moves 4 places right.

What is 6.02 × 10^23 written out?

602,000,000,000,000,000,000,000.

Is standard form the same as scientific notation?

In the UK, yes. In the US, standard form often means the ordinary written-out number.