Math 5 Lesson 19
- Classwork
- Decimal Fractions. Rational and Irrational Numbers
Definition: A rational number is a number that can be written as a fraction of two integer numbers $$p/q$$, where $$q≠0$$.
Definition: Any real number that is not rational is irrational. Irrational means that it can not be written as a ratio or two integers (rational number).
Examples:
π = 3.14159265358979323846264338327950288419716939937510…
e = 2.71828182845904523536028747135266249775724709369995…Definition: A set is countable if you can count the elements
Theorem: The set of rational number Q is countable.
Proof: 1. Convert the following fractions to decimals: a) 1 111 b) 3 7 c) −1 11 d)c) 5 9 e) 3 13 f) 2 5 g) 6 11 2. Convert the decimal fractions to the regular ones. 1 a) 0.251 b) −0.23123 c) 45.53 d) 2.5634 e) −1.32
1.2 Review
3. Solve
a)|3x + 5| + 2x = 4
b)| − x − 4| − 3x = 2
4. Solve
a) −3(2a + b) − 4(b + a)(4 − 3a)
b) 2(4a + −3b) − 2(4b + a)(4 − 3b) 2
2 Math 5 Lesson 19 Homework
2.1 Decimal Fractions. Rational and Irrational Numbers
1. Convert the following fractions to decimals:
a) 3
111
b) 1
8
c) −4
7
d)c) 5
6
e) 7
15
f) 2
7
g) 5
17
2. Convert the decimal fractions to the regular ones.
a) 0.165
b) −0.3525
c) 13.74
d) 2.1212
e) −1.21
2.2 Review
3. Solve
a)|4x + 6| − 3x = 5
b)| − 4x + 2| − 4x = 1
4. Solve
a) −3(5a + 2b) − 4(3b − 2a)(3 − 2a)
b) (7a + −7b) − 2(4a + b)(1 − 6b)
3 - Decimal Fractions. Rational and Irrational Numbers