# Scientific Notation

Concept

**Scientific notation** allows us to write very small or large numbers without having to write many zeros across the page. For instance, 0.000000000067 can be expressed as 6.7 x 10^-11 in scientific notation terms. See how much easier it is to write the latter in powers of base number 10? In this article, we will discuss on how to convert real numbers to scientific notation and vice versa.

## Converting Real Number into Scientific Notation

The number 139,000,000,000 can be written as 1.39 x 10^ 11.

The 1st number 1.39 is the coefficient and this has to be greater than or equal to 1 and less than 10.

The 2nd number 10^11 is the base. In scientific notation, this is always to the base of 10 and is written in exponential form.

Let us look at how we arrive at this.

Place the decimal point after the first digit and remove the zeros. This gives us the coefficient.

For the number 143,000,000 , the coefficient is 1.43 .

To determine the power of the exponent, we have to count the number of places from the decimal to the end of the zeros. For the number 143,000,000 , there are eight zeros so the base would be 10^8 .Thus, in scientific notation, the number 143,000,000 can be expressed as 1.43 x
10^8.

Scientific notation works almost the same for very small numbers. Just remember to add a negative sign to the power of the exponent. We can write one thousandth of a second as 0.001 or 1.0 x 10^-3.

## Converting Scientific Notation in Real Numbers

To change a scientific notation into a real number, we have to multiply its coefficient by its ten raised to the exponent given. For example, 1.56 x 10^4 would mean that we take its coefficient 1.56 and multiply it by 4 tens like this; 1.56 x 10 x 10 x 10 x 10 = 15600.Thus we have to move the decimal point to the right and add in the zeros accordingly.

For exponents that is negative, we move the decimal point to the left and add zeros in between the point and the first digit. For example, 3.47 x 10^-4 would become 0.000347.

'Try it Yourself' Section

If you wish to have some more practice, please try out the questions below

Convert the numbers into scientific notation and vici versa.

a) 111400000

b) 1.35 x 10^-7

Interesting note: Goggle, most popular online search engine, is derived from the term ‘googol'. This is 1 followed by a hundred zeros. In scientific notation, it's written as 1.0 x 10^100.

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