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Standard form calculator

7.25 x 10^5 is 725,000 in the standard form calculator: an exponent of 5 moves the decimal point 5 places right.

As an ordinary number725,000

Scientific notation
7.25 x 10^5
Engineering notation The exponent kept to a multiple of three, which is what the SI prefixes are built on.
725 x 10^3
SI prefix So the number reads as 725 kilo (k).
kilo (k)
Decimal point moved A positive exponent means a large number: the point moves right to restore it.
5 places left
E notation What a calculator display or a programming language prints.
7.25e5
Powers of ten and their prefixes
PowerNumberPrefix
10^121,000,000,000,000tera (T)
10^91,000,000,000giga (G)
10^61,000,000mega (M)
10^31,000kilo (k)
10^01-
10^-30.001milli (m)
10^-60.000001micro (u)
10^-90.000000001nano (n)
10^-120.000000000001pico (p)
  • Scientific notation requires a mantissa of at least 1 and less than 10. 47 x 10^3 is correct arithmetic and is not scientific notation; 4.7 x 10^4 is.
  • Significant figures are the point of the notation. Written as 4.70 x 10^4 the number claims three significant figures; 47,000 is ambiguous about whether the zeros are measured or placeholders.

How the Scientific Notation Calculator works

Standard form means two different things, depending on where you learned it.

In the US, standard form is a number written out in full: 725,000 rather than 7.25 x 10^5, and 0.00038 rather than 3.8 x 10^-4. Converting scientific notation to standard form means moving the decimal point. The exponent says how far: a positive exponent moves it right and a negative one moves it left, with zeros filling the gaps.

7.25 x 10^5: move the point 5 places right, 7.25, 72.5, 725, 7,250, 72,500, 725,000.

3.8 x 10^-4: move the point 4 places left, 3.8, 0.38, 0.038, 0.0038, 0.00038.

In the UK and much of the world, standard form is scientific notation itself: a number from 1 up to 10 times a power of ten, a x 10^n with 1 ≤ a < 10. To write a number in standard form in that sense, move the decimal point until one non-zero digit is in front of it and count the moves. 725,000 becomes 7.25 x 10^5, and 0.00038 becomes 3.8 x 10^-4. 72.5 x 10^4 is equal, but it is not standard form, because 72.5 is not below 10.

So "write the number in standard form" needs one look at the context. A US worksheet that gives 4.1 x 10^3 wants 4,100; a British exam that gives 4,100 wants 4.1 x 10^3.

Calculators and spreadsheets print a third version, E notation: 7.25E5 means 7.25 x 10^5, and turning it into standard form is the same decimal move.

Scientific Notation Calculator FAQ

What is 6.02 x 10^23 in standard form?

602,000,000,000,000,000,000,000: the 6.02 with its decimal point moved 23 places right, 24 digits in all.

What is 4.5 x 10^-3 in standard form?

0.0045. The negative exponent moves the decimal point 3 places left.

What does standard form mean for an equation?

Something else again. A linear equation in standard form is Ax + By = C, and a quadratic is ax^2 + bx + c = 0. The name is shared; the conversion is not.

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