Scientific Notation Calculator — convert a number to a × 10ⁿ

How it works

Scientific notation expresses any number as a single digit before the decimal point, times a power of ten:

x = a × 10ⁿ, where 1 ≤ |a| < 10

The mantissa a carries the significant digits; the exponent n records how big the number is (its order of magnitude). To find them:

• the exponent is n = ⌊log₁₀|x|⌋ — how many places the decimal point moves;
• the mantissa is a = x ÷ 10ⁿ, which lands it between 1 and 10.

A positive exponent means a large number (decimal point moves right); a negative exponent means a small one (moves left). It's the standard way to write the very large and very small numbers common in science.

Worked example

Convert 1234. Its order of magnitude is ⌊log₁₀ 1234⌋ = ⌊3.09⌋ = 3, so divide by 10³: 1234 ÷ 1000 = 1.234. Thus 1234 = 1.234 × 10³.

For a small number, 0.00456: the exponent is ⌊log₁₀ 0.00456⌋ = ⌊−2.34⌋ = −3, and 0.00456 ÷ 10⁻³ = 4.56, so 0.00456 = 4.56 × 10⁻³. And 9,200,000 = 9.2 × 10⁶.

Frequently asked questions

How do I write a number in scientific notation?

Move the decimal point until one non-zero digit remains in front of it — that gives the mantissa — and count the moves for the exponent. Moving left gives a positive exponent, moving right a negative one. 45,000 → move 4 places left → 4.5 × 10⁴.

What are the mantissa and exponent?

The **mantissa** (or coefficient) is the number part, always between 1 and 10; the **exponent** is the power of ten. In 6.02 × 10²³, the mantissa is 6.02 and the exponent is 23. Together they express the value compactly and make its size obvious at a glance.

How do I convert scientific notation back to a normal number?

Multiply the mantissa by 10 raised to the exponent — equivalently, shift the decimal point that many places (right for a positive exponent, left for a negative). 3.2 × 10⁵ shifts five places right to 320,000; 3.2 × 10⁻⁴ shifts four left to 0.00032.

What's the point of scientific notation?

It makes very large and very small numbers manageable and comparable. The speed of light (about 3 × 10⁸ m/s) and the size of an atom (about 1 × 10⁻¹⁰ m) are far easier to write and compare this way than as long strings of zeros. It also makes the number of significant figures explicit.

How does it relate to significant figures?

The mantissa shows exactly the significant figures. Writing 4.50 × 10³ signals three significant figures (the trailing zero counts), whereas 4500 is ambiguous. This is why scientific notation is the clearest way to state precision.

Is engineering notation the same thing?

Almost — engineering notation is a variant where the exponent is always a multiple of 3 (so the mantissa can range up to 1000), matching metric prefixes like kilo and milli. Scientific notation keeps the mantissa strictly between 1 and 10. This calculator uses standard scientific notation.