# Decimal numbers

Decimal is a term that describes the base-10 number system, probably the most commonly used number system. The decimal number system uses the following 10 numbers or symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The radix is thus 10. It is considered in Digital Electronics.

EXAMPLE 1: Decompose the number 734 into powers of 10

The decomposition of the number 734 takes the form:

734 = (7 × 10^{2}) + (3 × 10^{1}) + (4 × 10^{0})

= 734_{10}

EXAMPLE 2: Decompose the number 12345 into powers of 10

12345 = (1 × 10_{4}) + (2 × 10_{3}) + (3 × 10_{2}) + (4 × 10_{1}) + (5 × 10_{0})

= 12345_{10}

It’s Depending on position, each number is multiplied by the appropriate power of 10. The right-most digit represents the unit digit.

EXAMPLE3: Place values of a decimal number 526.979 are as follows:

- The place value of 6 is the units
- The place value of 2 is tens
- The place value of 5 is hundreds
- The place value of 9 is tenths
- The place value of 7 is hundredths
- The place value of 9 is thousandths

## How to Read a Decimal

An informal way to read a decimal is to first read the whole number as you would any whole number, then the decimal point as “point,” and finally each individual digit of the rational part.

For example, the number 17.59 would be read as “Seventeen point five nine”.

## Types of Decimals

There are two types of Decimals: Like decimals & Unlike decimals

### Like decimals

When there is exactly the same number of digits following the decimal point, two decimal numbers are said to be “like” decimals. For instance, the decimals 6.34 and 2.67 are Like decimals because they both include two digits following the decimal point.

### Unlike decimals

If there are differing amounts of digits following the decimal point in two decimal numbers, they are said to be “unlike” decimals. For instance, 5.3 and 6.873 are not decimals since they both have different numbers of digits following the decimal point.

**Interesting Facts and Notes on Decimals**

The prefix “deci” in the word “decimal” means ten.

Always add the decimal point after the ones place so that we can identify the starting point of the fraction.

Consider each digit starting from the right of the decimal point in order to compare the decimal or fractional part of any decimal number.

## How to Read a Decimal?

An informal method of reading a decimal involves reading the whole number part as usual, then stating “point” before reading each digit of the fractional part individually.

For instance, if we have the number 17.48, it would be read as “Seventeen point four eight.”

On the other hand, a more formal approach entails reading the whole number part, then stating “and” before reading the fractional part as a whole, considering the place value of the last digit.

For example, let’s consider the number:

25.678

Here, the whole part is 25, and the last digit’s place value, 8, corresponds to thousandths. So, the correct formal reading would be “Twenty-five and six hundred seventy-eight thousandths.”

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