How to quickly write numbers composed of many digits: standard notation and scientific notation, also called exponential, with practical examples.How to write numbers with many digits? This topic can be complicated, especially for those who are approaching this topic for the first time.
Let’s start from the beginning: a number is represented by its corresponding “numeral”, that is, a sequence of digits that uniquely identifies it.
For example : the numeral 15 represents only and exclusively the number fifteen. Except for a few basic rules, the enunciation of numbers versus the use of digits is largely a matter of writerly preference. Again, consistency is key, and policies and philosophies vary from medium to medium.
Different influential style and usage guides have different approaches, but in most cases it is recommended to write the numbers from zero to nine and use the next numbers after that, up to one million.
It is also recommended to write numbers from zero to one hundred and to use the subsequent digits, except for whole numbers used in combination with one hundred, one thousand, one hundred thousand, million, billion and beyond.
Having said this, let’s find out in more detail how to write numbers made up of many digits .
The composition of the numbers
In the decimal numbering system, the digits that make up a numeral take on a specific value based on the position they occupy ( positional system ).
In this numbering system the digits that can be used are: 0, 1, 2, 3, 4, 5, 6,7,8, 9.
The position criterion requires, for whole numbers, to divide the digits that make up a numeral into blocks of three starting from the digit furthest to the right. The first digit from the right will be: the unit , followed by the ten and the hundreds ; followed by thousands , tens of thousands , hundreds of thousands , millions , billions and so on.
The same concept applies to real numbers, dividing the digits to the right of the decimal point into blocks of three. Starting from the first one we have: tenths , hundredths , thousandths , etc. It is important to note that proceeding from right to left for the whole part each position is worth ten times as much as the one preceding it (1 ten is 10 units); the same applies to the decimal part (100 hundredths are equivalent to 10 tenths).
The exponential notation
An alternative to the classical numerical representation is offered by scientific (or exponential) notation. Consider the powers of 10: 10⁰ = 1; 10¹ = 10; 10² = 100, etc.
You can immediately notice that the result corresponds to the number 1, followed by as many zeros as the number exponent of 10.
Let’s now take the number 3,400,000 , which can be broken down as 3 x 1,000,000 + 4 x 100,000 . Represented using exponential notation, it becomes 3 x 10⁶ + 4 x 10⁵. It is clear that this type of representation is much more compact and easier to understand.
The same criteria apply to indicate the decimal part, raising the mantissa (10 in the example given) to a negative exponent. For example: 0.00001 becomes 1 x 10⁻⁵ .
