Scientific Notation Example

The scientific notation is writing numbers that are so big or so small, that it is more difficult to capture them with all their figures (sometimes these figures are zero 0). It is so called because in the fields of research and engineering numbers with precisions that can comprise dozens of digits and infinity of decimals are used.

The computers store the exact values, as they have been calculated, but display a value in scientific notation, so that laboratory workers develop their work faster. This is the case of the number Pi: π, whose approximate value is: 3.141592…

Scientific notation, like decimal notation, is based on the number 10 and its multiples. However, in this case exponents are used to summarize the multiples and submultiples of 10.

Scientific notation in large numbers

In numbers with more digits, and that are more difficult to write manually, multiples of 10 expressed with a base 10, raised to an exponent that covers all the figures.

For example:

100,000,000 (one hundred million) = 1 * 10⁸ (there are 8 figures that accompany the initial 1)

100,000 (one hundred thousand) = 1 * 10⁵ (there are 5 figures that accompany the initial 1)

The exponent indicates: both the times that 10 appears in a multiplication by itself, and the number of digits that accompany the initial.

• 10¹ = 10
• 10² = 10*10
• 10⁶ = 10*10*10*10*10*10
• 10⁸ = 10*10*10*10*10*10*10*10
• 10⁹ = 10*10*10*10*10*10*10*10*10

230,000,000 (two hundred thirty million) = 2.3 * 10⁸

345,500,000 (three hundred forty-five million, five hundred thousand) = 3,455 * 10⁸

Here the first figure is taken and a decimal point is put on it, to indicate the rest of the figures by scientific notation.

Scientific notation in small numbers

In numbers with more digits and that represent very small quantities, difficult to write manually, the submultiples of 10 are used expressed with a base 10, raised to anegative exponent that covers all the figures.

For example:

0.000001 (one millionth) = 1 * 10^-6

0.001 (one thousandth) = 1 * 10^-3

The exponent indicates the places that will be traveled to put the decimal point. In the empty spaces a zero 0 will be put.

• 10^-1 = 0.1
• 10^-2 = 0.01
• 10^-6 = 0.000006
• 10^-8 = 0.00000001
• 10^-9 = 0.000000001

0.00000023 (23 hundred millionths) = 23 * 10^-8

0.00003455 (three thousand four hundred fifty-five hundred millionths) = 3455 * 10^-8

Here the first figure is taken and a decimal point is put on it, to indicate the rest of the figures by scientific notation. It is named according to the last digit. In the examples above, 3 and 5.

• It may interest you: Decimal notation.

Examples of scientific notation

123000 = 1.23*10⁵

300000000 = 3*10⁸

4200000 = 4.2*10⁶

5200 = 5.2*10³

4938020000 = 4.93802*10⁹ = 493802*10⁴

0.00000014 = 14*10^-8 = 1.4*10^-7

0.002568 = 2568*10^-6 = 2.568*10^-3

0.00025603 = 25603*10^-8 = 2.5603*10^-4

0.0000108 = 108*10^-7 = 1.08*10^-5

0.000040056 = 40056*10^-9 = 4.0056*10^-5

Follow with:

• Decimal notation.