Notation

We all know that whole numbers can be extended indefinitely, but we can’t write such large numbers down on a piece of paper because they’re too big. Additionally, the numbers that appear at the millions place after the decimal point need to be expressed in a more straightforward manner. As a result, it is difficult to express a small number of integers in their enlarged form. As a result, we employ scientific notation. In addition, learn about Numbers in General Form.

Notation used in science

For example, 100000000 can be expressed as 108, which is the scientific notation for the number one million thousand thousand. The exponent in this case is positive. 0.0000001 is another extremely small integer that can be expressed as 10-8, where the exponent is negative.

The Definition of Scientific Notation

As explained in the introduction, the scientific notation allows us to represent numbers that are either extremely large or extremely small by multiplying single-digit values by ten and raising the result to the power of the exponent that corresponds to the number being represented. When the number is extremely large, the exponent is positive; when the number is extremely small, the exponent is negative. Learn about power and exponents to help you understand things better.

The following is an example of a broad representation of scientific notation:

The starting point should always be 10.

A non-zero integer exponent must be used; this means that the exponent might be either positive or negative.

The absolute value of the coefficient is more than or equal to 1, but it should be less than 10 in order for it to be considered significant.

It is possible to have coefficients that are either positive or negative numbers, including whole and decimal numbers.

The remainder of the number’s significant digits are contained within the mantissa.

Using the representation below, we can see how many places we need to shift the decimal point after the single-digit number in order to achieve the desired result.

If the given integer is a multiple of ten, the decimal point must be moved to the left, and the power of ten will be in the positive direction.

For example, the number 6000 = 6×103 is written in scientific notation.

If the specified value is less than one, the decimal point must be moved to the right, resulting in a power of ten that is negative.

Scientific notation, for example, is as follows: 0.006 = 6 0.001 = 6×10-3

Exemplifications of Scientific Notation

The following are some instances of scientific notation:

490000000 = 4.9108 1230000000 = 1.23109 

50500000 = 5.05 x 107

0.000000097 = 9.7 x 107 

0.0000212 = 2.12 x 10-5 

490000000 = 4.9108×108 

1230000000 = 1.23×109 

0.0000212 = 2.12 x 10-5

Exponents can be both positive and negative.

When huge numbers are stated in scientific notation, we employ positive exponents for base 10 to express them. For example, the number 20000 equals 2 x 104, where 4 is the positive exponent of the number.

Conclusion 

When small numbers are written in scientific notation, we utilise negative exponents for base 10 to express them. 0.0002, for example, is equal to 2 x 10-4, where -4 denotes the negative exponent.

In light of the foregoing, we can conclude that any number higher than one can be expressed as an expression with a positive exponent, but any number less than one can be written as an expression with a negative exponent.