How to write and speak the exponential notation

top

How to write and speak
the exponential notation

Exponential notation

Writing...

10³

10^3

1E3

1e3

2.7 × 10³

2.7 x 10^3

2.7E3

2.7e3

Speaking... "ten to the three"
"two point seven times ten to the three"
"two point seven ee three"

"Ten to the three" is short for the formal "ten raised to a power of three".
One also sometimes hears "ten to the third".

Some notational alternatives...

example What? Why

SI 4.8 × 10⁴ Exactly one non-zero digit to the left of the decimal. The standard for professional communication.

Order of
magnitude 0.48 × 10⁵ Exponent always indicates order of magnitude.
This is similar to SI when A < 3.16 (given some A × 10^x), but is 0.A × 10^x+1 when A > 3.16. The magnitude is immediately clear.

Exponent
on the left 10⁴ × 4.8
10⁵ × 0.48
The exponent, being the most significant "digit", is placed on the left.
Regular numbers are written with the most significant digit on the left. So with this layout, one doesn't have to skip to the end of the number just to see the exponent, and then have to remember it, as one jumps back to the beginning to see the digits. Either SI or Order-of-magnitude conventions can be used with this layout. Simplifies visual scanning.
Good for tables of numbers.

Common
magnitude 30. × 10⁴
4.8 × 10⁴
0.1 × 10⁴ A set of related numbers are given with the same exponent.
E.g., the sizes of the planets. Simplifies comparison.
Good for tables of related numbers (which are not too different in magnitude).

	example	What?	Why
SI	4.8 × 10⁴	Exactly one non-zero digit to the left of the decimal.	The standard for professional communication.
Order of magnitude	0.48 × 10⁵	Exponent always indicates order of magnitude. This is similar to SI when A < 3.16 (given some A × 10^x), but is 0.A × 10^x+1 when A > 3.16.	The magnitude is immediately clear.
Exponent on the left	10⁴ × 4.8 10⁵ × 0.48	The exponent, being the most significant "digit", is placed on the left. Regular numbers are written with the most significant digit on the left. So with this layout, one doesn't have to skip to the end of the number just to see the exponent, and then have to remember it, as one jumps back to the beginning to see the digits. Either SI or Order-of-magnitude conventions can be used with this layout.	Simplifies visual scanning. Good for tables of numbers.
Common magnitude	30. × 10⁴ 4.8 × 10⁴ 0.1 × 10⁴	A set of related numbers are given with the same exponent. E.g., the sizes of the planets.	Simplifies comparison. Good for tables of related numbers (which are not too different in magnitude).

A View from the Back of the Envelope
Comments encouraged. - Mitchell N Charity <mcharity@lcs.mit.edu>

Notes...

This is now perhaps too brief.

Could use mention of 10^-1, 10^-2, 10^-3,... being

"ten to the negitive one, two, three, ...", and assorted, perhaps less desireable, alternatives,

such as:	"one over ten to the one, two, three, ..."
	"one in ten to the one, two, three, ..."
	"one part per ten, hundred, thousand, ..."
	"one tenth, hundreth, thousanth"

Doables:
 Title isn't great.  Nor url.
 could use treatment of ± and ~
 information density is a bit low
 commentary on alternatives
 is 1/x = x^-1 mentioned somewhere?

History:
 2002.Mar.05  Changed × (&#215;) x symbols to × (&times;),
              to work around a reported Mac Netscape problem.
 1998.Sep.22  Added table of some notational alternatives.
 1997.Jul.27  First draft, pulling together scattered notes.