Scientific, Decimal and Engineering Forms

Formula and method

Round the number once to the chosen significant figures. Express that same rounded quantity as a scientific coefficient and integer exponent, a decimal expansion, and an engineering coefficient with an exponent divisible by three.

x ≈ m × 10^e, with1 ≤ |m| <10; engineering exponents are multiples of three.

Worked example

Enter these known values and leave the other values blank.

Assumptions and limitations

• Accept decimal/e literals and coefficient*10^integer notation, with no more than50 significant decimal digits. The verified domain is zero or finite magnitude1e-1000 through1e308.
• Choose a whole number from1 through15 significant figures. Halfway values round away from zero.64-digit working decimal arithmetic precedes display.
• The precision selector reveals or hides the precision input; hiding it preserves its current value. It does not disable rounding.
• All representations describe the same rounded quantity. Coefficient carry changes the exponent and engineering prefix when appropriate. Decimal expansions include trailing zeros according to the requested digit position.
• The captured sixteen prefixes from yocto through yotta are preserved. An engineering prefix appears only in the original supported nonzero bands1e-24≤|rounded x|<1 and1e3≤|rounded x|<1e27. Other magnitudes retain their scientific/e/expanded forms.
• Inputs accept decimal or e notation and bounded arithmetic expressions only when each intermediate and final value can be verified exactly as a finite decimal. Repeating fractions, functions, symbols and expressions that lose digits are rejected with guidance. Enter their finite decimal value instead; the calculator-specific magnitude and precision limits still apply.

Common questions

References

• Captured converter controls and sixteen prefix branches

Replace five captured binary/string numerical helpers with a local decimal scientific, rounded decimal and engineering computation. Preserve all original numerical controls, significant-figure choice and all sixteen SI-prefix variants. Correct decimal rounding at powers of ten, engineering truncation, coefficient carry and prefix selection after rounding; produce every representation from the same half-away-from-zero rounded quantity. Original helper JavaScript is pinned research evidence and is never evaluated in product. Bind the converter to its complete original capture and two atomic raw/authored compiled schemas. Accept decimal/e notation and provably exact bounded finite-decimal arithmetic expressions, with no more than50 significant decimal digits; use1 through15 significant figures, zero or magnitude1e-1000 through1e308, with64-digit working arithmetic. Preserve rounded expanded decimals using the already reviewed bounded Math35 formatter. Hiding precision controls retains the current precision value, exactly as captured. Invalid/cleared input withholds all five derived presentations.

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