Scientific Notation Converter

The rule: one digit before the point

Proper scientific notation has a coefficient of at least 1 and less than 10, multiplied by a power of ten. 45,200 is 4.52 × 10⁴. 0.000452 is 4.52 × 10⁻⁴. Values like 45.2 × 10³ are the same number but not in standard form — correct arithmetic, wrong presentation, and a mark lost in most exams.

Engineering notation and why it exists

Engineering notation restricts the exponent to multiples of three, so 45,200 becomes 45.2 × 10³. That maps directly onto the SI prefixes — kilo, mega, giga, milli, micro, nano — which is why component values and data rates use it. 4.52 × 10⁴ ohms means nothing at a glance; 45.2 kΩ is instantly readable.

Significant figures: what the zeros mean

Scientific notation solves an ambiguity that plain decimals cannot. Does 4,500 have two significant figures or four? You cannot tell. But 4.5 × 10³ has two, and 4.500 × 10³ has four, unambiguously. In any measured quantity the count of significant figures is a claim about precision — writing more than you measured overstates what you know.

Multiplying is the easy case

Multiply the coefficients, add the exponents, then renormalise if the coefficient leaves the 1–10 range. (3 × 10⁵)(4 × 10³) = 12 × 10⁸ = 1.2 × 10⁹. Addition is the awkward one: the exponents have to match first, which is why 10⁶ + 10³ is nowhere near 10⁹.

Frequently Asked Questions