[Alexa]

2016-1871

About 2016-1871.

2016-1871=?. 2016-1871=145. Yes.

[MSL]

1/2 + 1/4 + 1/8 + 1/16 + ⋯ = 1

  1/2 + 1/4 + 1/8 + 1/16 + ⋯ = 1.
 First six summands drawn as portions of a square:
^{By Hyacinth - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=21217220}.
 The geometric series on the real line:
<sup>Jim.belk - Own work

This picture illustrates the sum of a geometric series.

    Public Domain
    File:Geometric Segment.svg
    Uploaded: 24 September 2007</sup>.
https://en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%2B_%E2%8B%AF -- you may learn more from the source in Wikipedia.

[Gay]

Random numbers

Let me start with a randomness anecdote:

A: Give me 5 random numbers, please.

B: Sure. 777, 777, 777, 777 and 777.

A: Are you sure they're random?

A: One can never be sure when it comes to the randomness!

Random number from 1 to 6

If you need a random number from 1 to 6, I can use a die and here comes your random number: 2.

Random number from 1 to 4

Well, if you need a random number from 1 to 4, I can use random.org. Your random number is: 1.

Random number from 2 to 64

And, if you need a random number from 2 to 64, I will use again the same website. Your random number is: 13.

Random letters and numbers

There are not only random numbers, but random letters and random letters and numbers, too.

An example with a list randomizer:

There were 17 items in my list. Here they are in random order:

tttt
3
7
4
5
6
4twetwt
fsfsddfdsdf
b
d
n
v
c
rewrewr
vxcvcxcv
a
2

and the 2^nd one (I have randomized this list 2 times.):

vxcvcxcv
4twetwt
5
3
7
c
4
tttt
n
v
a
2
d
b
6
fsfsddfdsdf
rewrewr

Okay?

More random numbers from me:

Random six-sided dice:   6
Random number between 1 and 10:   9
Random lottery number between 1 and 42:   4
Random lottery number between 1 and 49:   20
Random number between 1 and 100:   38
Random number between 1 and 1000: 209
Random number between -100 and 100:   - 47.

[MSL]

A photo of a plastic flexible ruler

  When I was a schoolboy I never had the opportunity to have this interesting kind of ruler -- the flexible ruler. Here is a photo of a new flexible ruler: . I do really like it!

[MSL]

√4

√4. √4=2.

[MSL]

Equations and Formulas

  About the equations and formulas.

Equation

What is an equation?
 Well, an equation says that two things are equal. It will have an equals sign: "=", like this: x + 10 = 96. That equation says: what is on the left (x + 10) is equal to what is on the right (96). So, an equation is like a statement "this equals that". (Note: This equation has the solution x = 86.
 More examples:

• x + 1 = 2
• x - 100 = 8

I hope that it's easy and clear for you, dear math learners!

Formula

What is a formula? OK, it is just a special type of equation that shows the relationship between different variables. An example with a very popular and easy formula: a² + b² = c².

[SEO]

Nice. Now let's learn more about the math formulas.

They show the relationship between different variables.

An example: the formula for finding the volume of a cuboid is:

V = lwh

V stands for volume, l for length, w for width, and h for height.

When l=55, w=20, and h=10, then:

V = 55 × 20 × 10 = 11000

So, a variable is a symbol like V (or x) that stands in for a number we don't know yet. (A variable is a symbol that represents a quantity in a mathematical expression, as used in many sciences.)

[SEO]

Percentage

Percentage -- it is a number or ratio expressed as a fraction of one hundred (100). It's often denoted using the percent sign (%), or the abbreviations "pct.", "pct"; sometimes the abbreviation "pc" is also used. A percentage is a dimensionless number (pure number).

For example, 49% (read as "forty-nine percent") is equal to ​⁴⁹⁄₁₀₀, 49:100, or 0.49. Percentages are often used to express a proportionate part of a total.

From 0% to 100%

0% = 0 (0.00)
1% = 0.01
2% = 0.02
3% = 0.03
4% = 0.04
5% = 0.05
6% = 0.06
7% = 0.07
8% = 0.08
9% = 0.09
10% = 0.10
11% = 0.11
12% = 0.12
13% = 0.13
14% = 0.14
15% = 0.15
16% = 0.16
17% = 0.17
18% = 0.18
19% = 0.19
20% = 0.20
21% = 0.21
22% = 0.22
23% = 0.23
24% = 0.24
25% = 0.25
26% = 0.26
27% = 0.27
28% = 0.28
29% = 0.29
30% = 0.30
31% = 0.31
32% = 0.32
33% = 0.33
34% = 0.34
35% = 0.35
36% = 0.36
37% = 0.37
38% = 0.38
39% = 0.39
40% = 0.40
41% = 0.41
42% = 0.42
43% = 0.43
44% = 0.44
45% = 0.45
46% = 0.46
47% = 0.47
48% = 0.48
49% = 0.49
50% = 0.50
51% = 0.51
52% = 0.52
53% = 0.53
54% = 0.54
55% = 0.55
56% = 0.56
57% = 0.57
58% = 0.58
59% = 0.59
60% = 0.60
61% = 0.61
62% = 0.62
63% = 0.63
64% = 0.64
65% = 0.65
66% = 0.66
67% = 0.67
68% = 0.68
69% = 0.69
70% = 0.70
71% = 0.71
72% = 0.72
73% = 0.73
74% = 0.74
75% = 0.75
76% = 0.76
77% = 0.77
78% = 0.78
79% = 0.79
80% = 0.80
81% = 0.81
82% = 0.82
83% = 0.83
84% = 0.84
85% = 0.85
86% = 0.86
87% = 0.87
88% = 0.88
89% = 0.89
90% = 0.90
91% = 0.91
92% = 0.92
93% = 0.93
94% = 0.94
95% = 0.95
96% = 0.96
97% = 0.97
98% = 0.98
99% = 0.99
100% = 1 (1.00)

X%

X% (x%) means ?% (unknown percentage).

[MSL]

  Leo (Lele) "invented" this kind of percentage "c%". Well, imagine these combinations (alphabetical percentage ):
a%, b%, c%, d%, e%, f%, g%, h%, i%, j%, k%, l%, m%, n%, o%, p%, q%, r%, s%, t%, u%, v%, w%, x% (it was mentioned above already), y%, z%.

[SEO]

70/12

70/12. 70/12 (70÷12) = 5.83333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333(3).

[MSL]

48 - 88 = ?

 48 - 88 = x. x = -40, i. e. 48-88 = -40.

[SEO]

Factorial

Well, in mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040. As you see, the factorial function (symbol: !) means to multiply a series of descending natural numbers. Another example: 4! = 4 × 3 × 2 × 1 = 24.
The value of 0! is 1, according to the convention for an empty product. Zero Factorial is really interesting, because it's generally agreed that "0! = 1". It may seem funny and it's, imho, really funny, that in this case multiplying no numbers together (nothing) results in 1, but it helps simplify a lot of equations.
 So, the rule is simple, it's: n! = n × (n−1)! (which says "the factorial of any number is that number times the factorial of (that number minus 1)" That's why: 10! = 10 × 9! and 120! = 120 × 119!, etc.)

A factorial list:

n   n!
0   1
1   1
2   2
3   6
4   24
5   120
6   720
7   5,040
8   40,320
9   362,880
10   3,628,800
11   39,916,800
12   479,001,600
13   6,227,020,800
14   87,178,291,200
15   1,307,674,368,000
16   20,922,789,888,000
17   355,687,428,096,000
18   6,402,373,705,728,000
19   121,645,100,408,832,000
20   2,432,902,008,176,640,000
21   51,090,942,171,709,440,000
22   1,124,000,727,777,607,680,000
23   25,852,016,738,884,976,640,000
24   620,448,401,733,239,439,360,000
25   15,511,210,043,330,985,984,000,000

It's so cool!

[MSL]

30000/12

30000/12 = x. x = 2500 (i. e. 30000÷12=2500).

[MSL]

5% of 1000

5% of 1000. 5% of 1000 is? 5% of 1000 is 50 (5% of 1000 = 50; 5% * 1000 = 50).

[MSL]

20% of 50

20% of 50. 20% of 50 is? 20% of 50 is 10 (20% of 50 = 10; 20% * 50 = 10).