﻿ Decimal number — Math18

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# Decimal number

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## What are decimal numbers?

Decimal numbers are the values that represent numbers smaller than the unit, each decimal number has an integer and a decimal part, where the whole part is to the left of the decimal point and the decimal part to the right.

A decimal number is an approximate value that allows you to represent a rational and irrational number at an approximate value.

Note: Depending on the author the decimal point is represented by a point (18.18) or represented by a comma (18,18), to avoid confusion it is preferable to use the point.

## Which they are the decimal numbers?

Depending on the result we can classify the decimal numbers in different ways:

• Exact decimal numbers: They are those that have a number of specific decimal numbers or in other words have a final number in the decimal part, for example:

0.5
12.5843
138.54

• Periodic Decimal Numbers: They are those that have an unlimited or infinite number of decimal cider and the decimal part has a certain pattern or period. Periodic decimal numbers in turn are classified as pure and mixed:
Pure periodic decimal numbers: There is a period or pattern from the first decimal place, for example:

3.555555... Periodic = 5
13.181818... Periodic = 18
154.123123... Periodic = 123

Mixed periodic decimal numbers: The first decimal figures do not present a pattern or period but after some figures it begins to show a period, for example:

23.622222... Periodic = 2
5.135838383... Periodic = 83
245.01203010101... Periodic = 01

• Decimal numbers not periodic: They are decimal numbers of infinite numbers but do not have a defined pattern, corresponds to irrational numbers, such as the number pi, square root of 2, etc.

## Identify the amount it represents

Ones units (A), tens (B), hundreds (C) and thousand units (D) are aligned to the left of the point; to the right of the point the tenths (E), hundredths (F) and thousandths (G) are aligned.

DCBA . EFG 1 3 5 4 . 4 5 6

We have as a result: 1 thousand units, 3 hundreds, 5 tens and 4 ones to the left of the point; to the right of the point we have: 4 tenths, 5 hundredth and 6 thousandths.

## How do you read decimal numbers?

To say the amount of a number or to represent in written form it is possible by two common methods.

1. Common mention of the number and the point of division, for example:

25.67 → Twenty-five point sixty-seven.
0.47 → point forty seven.
100.100 → One hundred point one.
18.18 → eighteen point eighteen.

2. By positioning the last number to the right of the point, for example:

25.67 → Twenty-five integers, sixty-seven hundredths.
0.47 → forty seven hundredths.
100.100 → One hundred integers, one tenth.
18.18 → eighteen integers, eighteen hundredths.

Note: Instead of writing "integers" it can be represented as "units."

## Operations with decimal numbers

The four operations with fundamental decimals are addition, subtraction, division and multiplication.

### Addition and Subtraction with decimal point

When making sums with numbers with decimals, it is important to align the numbers according to the position of each number: The ones must be with the ones, tens with tens corresponding to the left of the point, to the right of the point must be the tenths with tenths, hundredths with hundredths and so on.

Examples:

+
2.2 5.6 / 7.8
+
8.4   3.3 / 11.7
-
68.7 22.7 / 46.0
-
364.67 187.38 / 177.29

### Multiplication with decimal point

When multiplying a number it is important to consider at the end of the operation the position of the point, for the placement of the point the spaces to the right of the decimal point of the numbers that are being multiplied are counted.

Examples:

A)
+
3.2   x25 /   160   64   80.0
B)
+
3.2  x2.5 /   160   64   8.00

The red number represents the offset of the point.

### Division with decimal point

The divisions with decimal point are very simple, we just have to place the decimal point in the quotient part, in other words the point goes up from the dividend to the quotient.