gizmobench

Scientific Notation Converter

Convert between standard, scientific and engineering notation, with significant figures preserved and the SI prefix named. Nothing passes through a floating-point number, so very large and very small values expand digit for digit.

Scientific · 2 significant figures4.2 × 10⁻⁴0.00042 · engineering 420 × 10⁻⁶ · 420 micro
Value
Show as
  • Scientificmantissa in [1, 10)
    4.2 × 10⁻⁴
  • Engineeringexponent a multiple of 3, so it maps to an SI prefix
    420 × 10⁻⁶
  • Standardwritten out in full, no exponent
    0.00042
  • E-notationwhat code and spreadsheets use
    4.2e-4
  • SI prefixµ = 10⁻⁶
    420 micro (µ)
  • Significant figures1.200 × 10³ has four; 1.2 × 10³ has two
    2
  • Order of magnitudethe leading digit sits at 10⁻⁴
    -4

Engineering notation pads the mantissa to 420 so the exponent can be a multiple of three. Only 2 of those digits are significant; the rest are placeholders, not measured figures.

Trailing zeros carry meaning. 1.200 × 10³ states four significant figures; 1.2 × 10³ states two. Converters that normalise through a float lose that distinction, which changes what the number claims about its own precision. Nothing here goes near a float: every form above is built digit by digit from what you typed.

Common questions

What is the difference between scientific and engineering notation?
Scientific notation keeps the mantissa between 1 and 10, so 0.00042 is 4.2 × 10⁻⁴. Engineering notation keeps the exponent a multiple of three, so the same number is 420 × 10⁻⁶, which maps directly onto SI prefixes, making it 420 microunits. Engineers prefer the second because it matches how components and units are actually labelled.
Why do trailing zeros change the significant figures?
Because they carry information about precision. 1.200 × 10³ states four significant figures, so the measurement was good to the nearest unit. 1.2 × 10³ states two. Both equal 1200, but they claim different things about how well you know it. Converters that normalise through a float lose that distinction silently, which is a real loss when the number came from an instrument.
How many significant figures does 1200 have?
By the standard convention, two. Trailing zeros in a whole number with no decimal point are treated as placeholders. If you mean four, write 1200. or 1.200 × 10³. This is genuinely ambiguous in plain notation, which is why the tool states the reading it used rather than picking silently.
Can it handle exponents beyond what a computer normally allows?
Yes. A double-precision number gives up around 10³⁰⁸ and underflows near 10⁻³²⁴. Because this works on the digit string rather than a float, values like 1 × 10¹⁰⁰⁰ expand correctly and round-trip exactly. That matters for physics and cryptography work where the magnitudes leave normal numeric ranges.
What input formats are accepted?
Standard decimals, E-notation in either case (4.2e-4 or 4.2E-4), and explicit forms with × 10^ or x10^. A mantissa outside 1 to 10 is normalised for you, so 42 × 10⁻⁵ is accepted and reported as 4.2 × 10⁻⁴.
What is the order of magnitude?
The exponent once the number is in scientific notation, the power of ten that describes its scale. It is the quantity you want when comparing two numbers roughly: something with order of magnitude 6 is about a thousand times larger than something with order of magnitude 3, regardless of the digits.

Every conversion is exact. The arithmetic is performed on the digits as typed, so nothing rounds, overflows or underflows at any magnitude. The one judgement call is how many significant figures a trailing-zero integer like 1200 carries; the standard convention says two, and the result says which reading it used.