🍫 What is a decimal?
Imagine that you are dividing a chocolate bar into 10 pieces. You ate three pieces. To say that you ate 0 chocolates is not true. To say that 1 is also incorrect. You ate part of the whole.
It was for situations when whole numbers were not enough that ordinary fractions were invented. And their most convenient form for recording is decimal fractions. We see them everywhere: on price tags (99.90 rubles), in thermometers (36.6 °C) or on scales (1.5 kg).
Definition
A Decimal is a way of writing a number where the integer and fractional parts are separated by a comma. The main feature: the denominator of such a fraction always contains 10, 100, 1000, and so on, but this denominator is not written, but is implied by the position of the number after the decimal point.
Anatomy of a number: breaking it down into pieces
Let's take the number 12,345 as an example. It consists of three elements:
- 1. Whole part (12)
It is to the left of the comma. This is a regular integer showing full units. - 2. Comma (,)
The boundary separating the “world of wholes” from the “world of parts.” - 3. Fractional part (345)
It's on the right. Shows what fraction of a unit we took. If there is no integer part, zero is written (for example, 0.5).
The magic of discharges
In integers, the further to the left the number, the greater its "weight" (units, tens, hundreds). In fractions everything is mirrored. The position of the digit after the decimal point is called digit:
| Position | Division name | Example at 12,345 |
|---|---|---|
| 1st digit | Tenths (1/10) | 3 (three tenths) |
| 2nd digit | Hundredths (1/100) | 4 (four hundredths) |
| 3rd digit | Thousandths (1/1000) | 5 (five thousandths) |
This whole system works on degrees of the number 10.
🗣 How to read fractions correctly?
The algorithm is simple: we read an integer + the word “integers” + a fraction + the name of the least significant digit.
- 7.5 - Seven point five, five tenths.
- 14.21 - Fourteen point twenty one hundredth.
- 0.125 - Zero point one, one hundred twenty-five thousandth.
Connection with ordinary fractions
A decimal fraction is not a new type of numbers, but simply a convenient notation for ordinary fractions. It's easy to convert them into each other:
Rule: How many digits after the decimal point, so many zeros in the denominator.
- 0.7 (1 digit) = 7/10
- 0.25 (2 digits) = 25/100
- 1.45 = 1 45/100 (or as improper fraction 145/100)
Types of decimals
Not all numbers divide nicely. There are two types of fractions:
- End: The numbers end (0.5 or 2.75). They can be reduced and converted into a regular fraction.
- Infinite (periodic):When we divide 1 by 3 we get 0.3333... Threes never end. This is written as0,(3). Read more about this in the section on the theory of fractions.
Frequently asked questions (FAQ)
❓ What to put: a comma or a period?
In Russia and most European countries, the comma (12.5) is used. In English-speaking countries (USA, UK) and in programming they usedot (12.5). This does not change the meaning of the number.
❓ Can a decimal fraction not have a whole part?
Formally, the whole part is always there. Even if you only took "half", you must write 0before the comma (0.5). Omitting a zero (writing .5) is accepted only in some foreign standards, but at school this is considered an error.
❓ Does the number change if you add zeros at the end?
No. In decimals, the zeros on the right have no meaning. 0.5 = 0.50 = 0.500. It’s like saying “half a meter” or “50 centimeters” - the length is the same.