1.2.2 Rational numbers
All the numbers that we use in our normal day-to-day activities are called Real Numbers. Real numbers are: Positive integers (1, 2, 3, 4, etc.) Fractions (1/2, 2/3, 1/4, etc). [The integers are really forms of fractions (1/1, 2/1, 3/1, etc.)] Negative numbers (-1, -3/4, etc.)
Any numbers that can be written in the form a/b where a and b are whole numbers are called Rational Numbers.
A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers. The number 6 is a rational number because it can be written as the fraction 6/1 Likewise, 1/4 is a rational number because it can be written as a fraction
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For example, astronomers measure the distance to stars in light years, a unit of distance which conveniently expresses the huge distances that are involved. A light year is the distance which light travels in one year. Let us see how many metres there are in one light year. Light travels at a speed of 300000000 m/s (three hundred million metres per second) = 9 460 800 000 000 000 m per year! This number is very inconvenient to read and to write. The solution to this problem is to write such very large (or very small) numbers in scientific notation.
Scientific notation makes representing units of any size easy.
Scientific notation involves writing a number as the product of two numbers. The first one, the digit value, is always more than one and less than 10. The other, the exponential term, is expressed as a power of 10. There is only one digit to the left of decimal comma.
So, instead of writing that the diameter of an atom of lead is 0, 000 000 000 32 m you would write:
3, 2 × 10-10 m
A number that is smaller than 1 is represented as something multiplied by