Scientific Notation Converter

The formula

Mantissa

The coefficient, always at least 1 and below 10 in normalised form.

Exponent

The power of ten. Positive shifts the decimal point right, negative shifts it left.

e notation

The way an exponent is written on a keyboard: 4.7e-4 means 4.7 × 10⁻⁴.

Worked example

Converting 0.00047 to scientific notation, then 6.02e23 back to decimal.

• log₁₀(0.00047) = −3.328 → floor = −4
• Mantissa = 0.00047 ÷ 10⁻⁴ = 4.7
• Result: 4.7e-4
• Reverse: 6.02e23 = 6.02 × 10²³ = 602,000,000,000,000,000,000,000

0.00047 = 4.7e-4; 6.02e23 = 602 sextillion.

Counting decimal places is the same thing as the exponent

The exponent is just how far the point moved. From 0.00047 to 4.7 the point travels four places right, which is why the exponent is −4 — a negative exponent means the original number was smaller than one. From 602,000 to 6.02 it travels five places left, giving 6.02e5. Doing it by counting is faster than reaching for a logarithm, and the calculator is there to check you.

Normalised form keeps the mantissa between 1 and 10

Writing 47e-5 and 0.47e-3 both describe the same quantity as 4.7e-4, but only the last is normalised. Standard form matters because it makes magnitudes directly comparable at a glance — the exponents line up and you can see immediately that 4.7e-4 is a thousand times larger than 4.7e-7 without reading a single zero.

Multiplying and dividing get easy in this form

Multiply the mantissas and add the exponents; divide the mantissas and subtract the exponents. So 3e8 × 2e-3 is 6e5. Then renormalise if the mantissa leaves the 1-to-10 range: 5e4 × 4e4 gives 20e8, which is written 2e9. Doing arithmetic this way keeps very large and very small numbers manageable without a single trailing zero.

Where the precision limits sit

The tool carries 15 significant figures, which is the practical limit of double-precision arithmetic. Beyond about 10³⁰⁸ a value overflows to infinity, and very small values eventually lose precision as they approach the smallest representable number. For everyday scientific and engineering magnitudes this is far more headroom than needed, but it is why a mantissa can occasionally show a long tail of digits instead of a clean value.

Common questions

How do I write a number in scientific notation?

Move the decimal point until exactly one non-zero digit sits in front of it, then count how far it moved. That count is the exponent — positive if you moved it left, negative if you moved it right. 0.00047 becomes 4.7 × 10⁻⁴, and 602,000 becomes 6.02 × 10⁵.

What does e mean in a number like 4.7e-4?

It stands for times ten to the power of, so 4.7e-4 is 4.7 × 10⁻⁴, which is 0.00047. It is a keyboard-friendly way to write an exponent and is what calculators and programming languages use.

Which direction will the tool convert?

It looks for the letter e in what you type. If e is present it treats the input as scientific notation and returns a decimal; otherwise it treats it as a plain number and returns scientific notation. Commas in a plain number are ignored, so 602,000 works.

Why does a negative exponent mean a small number?

Because a negative power of ten is a division rather than a multiplication. 10⁻⁴ is one ten-thousandth, so multiplying by it shifts the decimal point four places left. Any value with a negative exponent in normalised form is smaller than one.