8th Maths : Chapter 1 : Numbers : Summary

**SUMMARY**

• A number that can be expressed in the form *a/b *where** ***a *and** ***b*** **are integers and *b *≠* *0* *is called a rational number.

• All natural numbers, whole numbers, integers and fractions are rational
numbers.

• Every rational number can be represented on a number line.

• 0 is neither a positive nor a negative rational number.

• A rational number** a/b **is said to be in the standard form if its denominator

• There are
unlimited numbers of rational numbers between two rational numbers.

• Subtracting
two rational numbers is the same as adding the additive inverse of the second number
to the first rational number.

• Multiplying
two rational numbers is the same as multiplying their numerators and denominators
separately and then writing the product in the standard form.

• Dividing
a rational number by another rational number is the same as multiplying the first
rational number by the reciprocal of the second rational number.

• The following
table is about the properties of rational numbers (**ℚ**).

• 0 and 1
are respectively the additive and the multiplicative identities of rational numbers.

• The additive
inverse for *a/b* is –*a/b* and vice – versa.

• The reciprocal
or the multiplicative inverse of a rational number *a/b* is *b/a* since *a/b* × *b/a *= 1.

• A natural
number *n* is called a square number, if
we can find another natural number *m* such
that *n* = *m*^{2}.

• The square
root of a number *n*, written as √*n *(or)* n*^{1/2}* *, is the number that gives* n *when multiplied by itself.

• The number
of times a prime factor occurs in the square is equal to twice the number of times
it occurs in the prime factorization of the number.

• For any
two positive numbers *a* and *b*. we have

(i) √*ab* = √*a* × √*b* and (ii) √(*a/b*) = √*a*/√*b* (*b*≠0)

• If you
multiply a number by itself and then by itself again, the result is a cube number.

• The cube
root of a number is the value that when cubed gives the original number.

• An expression
that represents repeated multiplication of the same factor is called a power.

• The exponent
corresponds to the number of times the base is used as a factor.

• Laws of
Exponents: (i) *a ^{m}*

• Other
results: (i) *a*^{0} = 1 (ii) *a ^{−m}* = 1/

• To write
in scientific notation, we follow the form **S × 10 ^{a}** where

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