Number systems: Class 9 maths video

0:00 Class 9 maths. Number systems.

0:03 Welcome, young cadets, to another exciting mission with Captain Calc!

0:08 Today, we're diving deep into the secret world of Number Systems.

0:13 Meet the Number Family.

0:15 Natural numbers are for counting things like 1, 2, 3...

0:19 .

0:20 Try this one. Is 5 a rational number?

0:25 Yes. We can write 5 as 5/1.

0:28 This is a p/q form where p=5 and q=1, and q is not zero.

0:35 So the answer is Yes.

0:37 The Mysterious Irrationals.

0:40 Irrational numbers cannot be written as a fraction p/q.

0:45 Their decimal expansions are non-terminating (never end) and non-recurring (never repeat).

0:51 Try this one. Is √4 an irrational number?

0:57 First, simplify √4. √4 equals 2.

1:03 We can write 2 as 2/1. This is in p/q form. So it is rational.

1:09 So the answer is No.

1:11 Real Number Operations.

1:13 Real numbers are the collection of all rational and irrational numbers.

1:18 They cover every point on the number line.

1:22 Try this one. Simplify 2√3 + 5√3.

1:29 Treat √3 like a variable, for example 'x'.

1:34 Add the coefficients: (2+5)√3.

1:39 The result is 7√3.

1:42 So the answer is 7√3.

1:46 Exponent Power-Ups.

1:48 Recall the laws of exponents for integers, like a^m × a^n = a^(m+n) and (a^m)^n = a^(mn).

1:58 These laws also apply to real numbers and fractional exponents.

2:02 Try this one. Simplify 2³ × 2⁴.

2:08 Use the law a^m × a^n = a^(m+n).

2:13 So, 2^(3+4) = 2^7.

2:16 So the answer is 2^7.

2:19 Your turn. Find one rational number between 1/2 and 3/4. Pause the video, and try it.

2:29 The answer is 5/8.

2:32 Well done! Now try the practice and the quiz in this lesson on LearnFun.