Scientific Notation

• In countries that use the long scale (based on powers of a million) like Europe:

= 4.1 x 1012

• In countries that use the short scale (based on powers of a thousand plus one) like USA:

= 4.1 x 109

To convert the term into scientific notation, you need to shift some decimal places left/right to between the leading nonzero digit and the adjacent digit, so the value is in the form a x 10b where b is the integer and a is the constant.

Note that 86000 is interpreted as 86000.0. Shift 4 decimal places to the left from the starting point, so the exponent for base 10 is 4. Therefore, the value in scientific notation is 8.6 x 104.

To convert number from standard form to scientific notation, you need to shift the decimal places left/right right up to the one between the leading nonzero digit and the adjacent digit. For instance:

0.034

Shift 2 decimal places to the right to obtain:

3.4 x 10-2.

Well, to convert the number from scientific notation to standard form, shift the number of decimal places in the opposite way. For instance, if the exponent for base 10 is -2, and you want to convert it back to the standard form, you shift 2 decimal places to the left.