JEE Main Important Physics formulas
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To represent “19” in words, you have to understand the significance of “19” first. At first glance, “19” appears to be a number. Do you agree with me?
Imagine that you put some “unit of measurement” (like an mg, an ml, etc.) beside "19". It will, then, indicate some physical quantity (like "19 mg" of chocolate cake, or "19 ml” of oil).
As such, "19" as a number is made up of the digits 1, and 9; and every digit changes its meaning when its place value changes in a number. Isn’t it interesting? Let us dive into it to explore further.
At first glance, you find no unit of measurement with "19". So, "19" is nothing but a unitless number only.
It is worth noting that the English word for \[19\] is nineteen, and it is the nineteenth natural number.
Here, you have “2” digits in the number “19”.
Here, you have the following information about the place values of these 2 digits of 19.
The unit’s place in the number “19” is “9”.
The ten’s place in the number “19” is “1”.
Ten’s place value | Unit or One’s place value |
\[1\times 10\] | \[9\times 1\] |
Mathematically you can note the following
\[\begin{align}
1\times 10+9\times 1 \\
=10+9 \\
=19
\end{align}\]
Here, you notice that “19” has only two non-zero digits 1 and 9, in its ten’s place and unit’s place, respectively.
Thus, you get that "19" is written as “Nineteen ” in words.
In the term "19 rupees” you can easily, mark the unit "rupees" after the number "19".
You can easily express "19 rupees” in words, by placing the unit “rupees” after writing the number in words.
So, you infer that “19 rupees” is “Nineteen rupees” in words.
Whenever you get any number that “2” completely divides leaving no remainder, you call it an “even number”.
On the contrary, when you find that a number is not completely divisible by 2 but it leaves a remainder, you get an “odd number”.
The number “19” is not completely divisible by 2 as it leaves a remainder of 1 when you divide “19” by 2. As a result, you have \[19=9\times 2+1\] .
So, you can conclude that it is not an even number, but .an “odd number”.
In case you multiply any number by itself only once, the subsequent product is nothing but a “perfect square number”. Thus, “a perfect square” can also be seen as the product of two equal integers.
\[19=19\times 1\]
Here you can never express “19” in terms of the product of two equal integers. Hence, you get that “19” is not a perfect square.
On multiplying any number by itself twice, the product that you get is, basically, a “perfect cube number”. Look that a “perfect cube number” can be expressed in terms of the product of three equal integers.
\[19=19\times 1\]
Here, “19” cannot be expressed as the resultant product of three equal integers. Therefore, “19” is, in no way, a perfect cube.
When you find any number that on factorizing results in only two factors (“1”, and the number itself), you get a “prime number”. Inversely, a number with more than two factors is a “composite number”.
\[\text{Factors of 19}=\ 1,\ 19\]
Here you achieve that the number “19” has only two factors 1 and 19. Thus, you deduce that “19” is not a composite number, but a “prime number”.
You know that any natural or counting number is a cardinal number.
The number “19” is, definitely, a specific counting number; therefore, it is a “cardinal number”.
Whenever, you find that any number is used to designate any place or position in a set, series, or collection; you get an “ordinal number”. It, generally, uses the extension “st” or “rd” or “th” (as applicable) after the numeric value. For example 1st, 2nd, 3rd, 4th, and so on.
Therefore, you can write “19th” which indicates an “ordinal number”.
You know that a perfect cube number is a product of two equal real numbers.
\[19=19\times 1\]
By inspection, you notice that “19” is the required minimum positive integer that you should multiply by “19” to obtain your desired perfect square, in the following way.
\[\begin{align}
19\times 19 \\
={{19}^{2}} \\
=361
\end{align}\]
Thus, “19” is the required minimum number.
In the decimal number system, every number is defined in terms of the place value of its constituting digits, taking the reference from its right-hand most digit.
You will notice that the place value of a digit increases as “powers of 10” on moving to the left-hand side from the right-hand most or the first digit of the number.
Thousandth place value | Hundredth place value | Ten’s place value | Unit or One’s place value |
\[\times 1000\ \text{times}\] | \[\times 100\ \text{times}\] | \[\times 10\ \text{times}\] | \[\times 1\ \text{time}\] |
Thus you get the following
\[\begin{align}
190=1\times 100+9\times 10+0\times 1 \\
=100+90+0 \\
=\text{one hundred and ninety} \\
1900=1\times 1000+9\times 100+1\times 10+0\times 1 \\
=1000+900+10+0 \\
=\text{one thousand and nine hundred}
\end{align}\]
As the number “19” exists in the set of integers in the number line, it is an “integer”. \[Z=\left\{ -\infty ,\ \ldots ,\ -3,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3,\ \ldots +\infty \right\}\]
When you consider “19” as the real part and, “0” as its imaginary part, you can, definitely, express “19” as a complex number in the following way .
\[19=19+i.0\]
Note that the number “19” can be represented in the fractional form of “p/q”, where p and q fall under integers and, q is non-zero. So, by definition, “19” is a rational number.
\[\begin{align}
19=\frac{19}{1} \\
=\frac{p}{q},\text{where}\ p=19,\ q=1\left( \ne 0 \right)
\end{align}\]
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