Scientific notation calculator

One value, three useful forms

Use this calculator to read a small decimal, shorten a very large number, or check arithmetic involving powers of ten. It is useful for students checking a worked example, teachers preparing an answer, and anyone moving a value between a written calculation and a spreadsheet. Conversion shows scientific notation, E notation and ordinary decimal notation together. These are different ways to write the same result, subject to the rounding you select.

Choose Convert one number for either direction: enter 0.00045 to get scientific notation, or enter 4.5e-4 to recover the decimal. For arithmetic, choose Add, Subtract, Multiply or Divide and fill both A and B. Subtraction means A minus B; division means A divided by B. Select the maximum significant digits, then press Calculate or Enter. Editing an input or setting clears the previous result so it cannot be mistaken for an updated answer.

Entering decimals and powers of ten

Use a decimal point and omit grouping separators in every language. Accepted examples include -12.5, .004, 6.02E23 and 4.5 × 10^-4. The forms 4.5x10^-4 and 4.5*10^-4 also work. The exponent after E or after the caret must be a whole number; e means “times ten to the power” here, never Euler’s constant. A negative sign before the coefficient changes the sign of the number. A negative exponent instead describes a small magnitude.

Each input allows up to 200 coefficient digits, including zeros, and 300 total characters. The explicitly entered exponent must lie between -10000 and 10000. Remove units, commas, fractions, parentheses and multi-operation expressions. This is a two-number calculator, not an expression parser. If a field is invalid, its message identifies the correction and the other input is preserved.

What the calculation steps mean

A nonzero number in normalized scientific notation has the form a × 10^n, with 1 ≤ |a| < 10 and an integer n. For zero, this calculator uses 0 × 10^0. Changing the coefficient requires an opposite change in the exponent to preserve the value: 45 × 10^-5 becomes 4.5 × 10^-4.

Addition and subtraction first align the powers of ten. Multiplication multiplies coefficients and adds exponents; division divides coefficients and subtracts exponents. The steps show the normalized inputs, the corresponding operation and the final normalization. Decimal integer arithmetic retains the entered values exactly until final rounding, including large exponent differences and cancellation. A division may have an endless decimal expansion, so its displayed answer can still be approximate.

Worked examples to check

Example 1 — convert 0.00045 with the default 15-digit limit. The result is 4.5 × 10^-4, or 4.5e-4, and decimal 0.00045. Moving the decimal four places to form the coefficient gives a negative exponent because the original value is smaller than one.

Example 2 — multiply A = 3e4 by B = 2e6. The coefficients give 3 × 2 = 6 and the exponents give 4 + 6 = 10. The exact result is 6 × 10^10, or decimal 60000000000. Example 3 — add 4e5 and 7e4: rewrite the second value as 0.7 × 10^5, then add to obtain 4.7 × 10^5. Adding the exponents would give the wrong answer.

Precision, output and practical limits

The default limit is 15 significant digits; choose any whole number from 1 to 50. Rounding happens once at the final result, with halfway values rounded away from zero. For instance, converting -1.25 at two digits gives -1.3. Dividing 1 by 3 at six digits gives 3.33333e-1, marked Rounded result. Exact result means the displayed numeric value equals the calculation on your inputs, not that a physical measurement has no uncertainty.

Copy result and steps puts all displayed forms, the exact-or-rounded status and the operation into plain text. Numeric output always uses a decimal point without grouping, so check the receiving application’s import rules. Decimal expansions longer than 1,000 characters are omitted with an explanation; the scientific and E forms remain available. No calculation history is saved. Keep your original units and measurement assumptions separately when using an answer in notes or a report.

Are E notation and scientific notation equivalent?

Yes. 4.5e-4 and 4.5 × 10^-4 express the same value. E is a plain-text notation that avoids superscript formatting and is convenient for copying.

Why are commas rejected?

A comma can mean a decimal mark or a thousands separator. To avoid silently changing your number, this calculator requires a point for decimals and no grouping in all six languages.

Does the digit setting apply measurement significant-figure rules?

No. It limits output digits. Trailing zeros are removed, and the calculator does not infer uncertainty or the correct precision from measured inputs. Apply your course or measurement rules separately.

Can I divide by zero or calculate a whole formula?

Neither is supported. Zero as B in division produces a field error; zero as A is valid when B is nonzero. For a longer calculation, perform separate operations and avoid reusing rounded intermediate values when precision matters.

Why is there no long decimal result?

The value may need more than 1,000 characters in decimal form. This display limit is not an overflow error or a zero result. Use the compact E notation, and confirm the receiving software supports its exponent.