Scientific Notation Calculator
Type a number in any form — 0.00042, 6.02e23, 4.2 × 10^-4 — and get it in scientific notation, E notation and plain decimal, together with its significant-figure count. The other tabs multiply, divide, add and subtract directly in scientific notation.
The mantissa always sits between 1 and 10; a negative exponent means a value smaller than 1.
Formula and calculation
Worked example
The number 0.00042 carries 2 significant figures — the zeros in front of the 4 only mark the size. The decimal point moves four places to the right to leave one nonzero digit in front of it, so the value is 4.2 × 10^-4. Calculators and spreadsheets type the same number as 4.2e-4.
Significant figures: what the zeros are hiding
Writing a number in scientific notation makes its precision visible, because the mantissa is nothing but the meaningful digits. Leading zeros never count — 0.00042 has two significant figures, not six. Zeros between nonzero digits always count (1.008 has four). Trailing zeros are the ambiguous ones: in 1500000 they may be placeholders or real measurements, which is why the same number written as 1.500000 × 10^6 declares seven significant figures while 1.5 × 10^6 declares two. Counting matters because it decides how to report an answer: multiplying or dividing keeps the fewest significant figures among the inputs, while adding and subtracting keeps the fewest decimal places. The question this calculator prints after an operation is the result of that rule.
E notation, and typing powers of ten into anything
The letter E is a display convention, not a different number: 6.02e23 and 6.02 × 10^23 are the same value, and 6.02E23 with a capital E is the same again. It exists because calculators, spreadsheets and programming languages needed a compact, unambiguous way to write an exponent on a screen or a keyboard — it survives from the days when a calculator display had to say it in eight characters. When you see e in a computer context it always means × 10^, so 4.2e-4 is 0.00042 while 4.2e4 is 42000. This calculator accepts every spelling of it, including 4.2 × 10^-4 and 4.2x10^-4 pasted from a document, so you can paste a value straight from a lab report or a spreadsheet without rewriting it first.
What the results mean
- Scientific notation
- The number written properly in scientific notation, m × 10^n, with the mantissa m between 1 and 10 (zero itself is 0 × 10^0).
- E notation
- The same value in E notation, the ASCII shorthand calculators, spreadsheets and programming languages use: 4.2e-4 means 4.2 × 10^-4.
- Ordinary decimal
- The value written out in full as an ordinary decimal number, with no exponent — useful for checking a value against what you expected.
- Significant figures
- How many significant figures the number you typed actually carries: leading zeros never count, trailing zeros in a whole number with no decimal point do not count, and after an operation the answer keeps the fewest of the inputs.
- Calculation
- The conversion or the arithmetic spelled out — the decimal point shift for a conversion, or the mantissa and exponent rules for an operation.
Frequently asked questions
What is 0.00042 in scientific notation?
4.2 × 10^-4. Move the decimal point four places to the right until one nonzero digit stands in front of it, and the four places become a power of −4. In E notation the same value is written 4.2e-4, and it carries two significant figures.
How do I multiply and divide in scientific notation?
Multiply the mantissas and add the exponents, or divide the mantissas and subtract the exponents: (2 × 10^3) × (3 × 10^-4) = 6 × 10^-1, which is 0.6. If the mantissa you get is not between 1 and 10, shift it one place and adjust the exponent by one.
What is E notation?
E notation is the calculator-and-computer spelling of × 10^: the number before the E is the mantissa and the number after it is the exponent, so 6.02e23 means 6.02 × 10^23. It comes up because a screen or a plain-text file cannot easily show a superscript.
How many significant figures does 0.00042 have?
Two — the 4 and the 2. Zeros in front of the first nonzero digit only fix the position of the decimal point, so they never count. The same is true of 0.0000042: it also has two significant figures, however many zeros you write in front.
How do I add numbers in scientific notation?
Line them up on the same power of ten first, then add the mantissas: 2 × 10^3 + 3 × 10^-4 becomes 2000 + 0.0003 = 2000.0003, or 2.0000003 × 10^3. Adding the exponents directly, the way multiplication does, gives a wrong answer, so this calculator writes the numbers out in full when it adds or subtracts.