Scientific Notation Calculator — Convert Numbers to a × 10ⁿ

What Is Scientific Notation?

Scientific notation is a compact way to express very large or very small numbers. It is widely used in physics, engineering, chemistry, astronomy, and computing. A number written in scientific notation takes the form a × 10ⁿ, where:

• a (the significand or mantissa) satisfies 1 ≤ |a| < 10
• n (the exponent) is an integer — positive for large numbers, negative for small ones

Examples: the speed of light ≈ 3 × 10⁸ m/s; the mass of an electron ≈ 9.109 × 10⁻³¹ kg.

Scientific Notation Rules

• Move the decimal point until the number is between 1 (inclusive) and 10 (exclusive).
• Count the places moved: right moves give a negative exponent; left moves give a positive exponent.
• The mantissa must always satisfy 1 ≤ |a| < 10.
• Trailing zeros after the decimal are significant and should be kept according to significant-figure rules.

How to Convert a Number to Scientific Notation

Suppose we want to convert 0.00345 to scientific notation:

1. Place the decimal point after the first non-zero digit: 3.45
2. Count the places the decimal moved to get there: 3 places to the right
3. Because we moved right (making the number larger), the exponent is negative: n = −3
4. Write the result: 3.45 × 10⁻³

Another Example — Large Number

Convert 4,200,000 to scientific notation:

1. First non-zero digit: place decimal after 4 → 4.2
2. The decimal moved 6 places to the left → exponent is positive: n = 6
3. Result: 4.2 × 10⁶

E-Notation (Computer/Engineering Format)

Many calculators and programming languages write scientific notation using the letter e (or E) instead of the × 10ⁿ symbol:

• 3.45 × 10⁻³ → 3.45e-3
• 4.2 × 10⁶ → 4.2e+6
• Used in Python, JavaScript, C, Java, Excel, and scientific calculators.

Engineering Notation

Engineering notation is a variant of scientific notation where the exponent is always a multiple of 3 (…, −6, −3, 0, 3, 6, …). This aligns with SI prefixes (micro, milli, kilo, mega, etc.):

• 0.00345 m → 3.45 × 10⁻³ m = 3.45 mm
• 4,200,000 Hz → 4.2 × 10⁶ Hz = 4.2 MHz

Unit Support: Metric, US Imperial, and Currencies

This calculator supports units in three systems so you can attach the correct label to your scientific-notation result:

• Metric (SI): nm, μm, mm, cm, m, km (length); μg, mg, g, kg, t (mass)
• US Imperial: in, ft, yd, mi (length); oz, lb, ton (mass)
• World currencies: USD, EUR, GBP, JPY, CAD, AUD, CHF, CNY, INR, RUB, BRL, MXN

The unit is appended to the result for display purposes only — the numerical conversion is not affected.

FAQs

Why is 0 not written in scientific notation?

Zero has no first non-zero digit, so the standard form a × 10ⁿ breaks down. By convention, 0 is simply written as 0 (or 0 × 10⁰).

Can the mantissa be negative?

Yes. For a negative number like −0.00345, the mantissa is −3.45 and the exponent is −3, giving −3.45 × 10⁻³.

What is the difference between scientific notation and standard form?

In the United States "scientific notation" and "standard form" both refer to a × 10ⁿ. In the United Kingdom, "standard form" specifically means the same thing, while "scientific notation" is the international term. Our calculator uses both interchangeably.

How many significant figures should I use?

Use as many significant figures as your measurement precision allows. For instance, 3.45 × 10⁻³ has three significant figures, while 3.4500 × 10⁻³ has five.

What is the largest number the calculator handles?

PHP's floating-point range covers roughly ±1.8 × 10³⁰⁸, which is more than sufficient for any practical scientific or engineering application.