Why does engineering notation allow a mantissa above ten?

Because it fixes the exponent to multiples of three so it maps onto metric prefixes. 123,456 becomes 123.456 times ten cubed, which reads as 123.456 kilo of whatever the unit is.

Math & Statisticsnotation

Scientific Notation Converter

A number in scientific and engineering notation. Engineering notation keeps the exponent a multiple of three so it lines up with the metric prefixes, which is why instruments use it.

Also called: standard form calculator, engineering notation.

Scientific notation

1.2346 x 10^5

123,456 is 1.2346 x 10^5. In engineering notation, where the exponent is always a multiple of three, it is 123.456 x 10^3.

Engineering notation

123.456 x 10^3

Mantissa

1.23

Exponent

Order of magnitude

How this is calculated

Method and background

How this is calculated

Scientific notation puts exactly one non-zero digit before the point, so the exponent reads directly as the order of magnitude. Engineering notation relaxes that to keep the exponent divisible by three, which means the mantissa can run up to a thousand but the exponent always matches a prefix: kilo, mega, giga, milli, micro. That is the whole reason both conventions exist.

value = mantissa * 10 ^ exponent, with the mantissa between 1 and 10

m: Mantissa
e: Exponent

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a six-figure number

Number: 123,456
Decimal places in the mantissa: 4

Scientific notation1.2346 x 10^5

arithmetic identity

Open this example

a small number has a negative exponent

Number: 0
Decimal places in the mantissa: 4

Scientific notation3.4 x 10^-4

boundary

Open this example

zero has no exponent

Number: 0
Decimal places in the mantissa: 4

Scientific notation0

degenerate case

Open this example

Method and limits

What it assumes

A finite real number.

What it deliberately does not model

Numbers beyond about 1e308 cannot be represented and are declined.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

Why does engineering notation allow a mantissa above ten?: Because it fixes the exponent to multiples of three so it maps onto metric prefixes. 123,456 becomes 123.456 times ten cubed, which reads as 123.456 kilo of whatever the unit is.