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A decimal is a numerical system used to represent numbers in base 10, which is also known as the decimal base. It is the most commonly used numerical system in everyday life, and it’s the system we use for counting, measuring, and performing arithmetic operations. In the decimal system, numbers are represented using ten distinct digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These digits are used to create all possible numerical values through various combinations.

### Place Value System

The decimal system relies on the concept of place value, which means that the value of each digit in a number is determined by its position or place within the number. Each position represents a power of 10. The rightmost position is the units place, followed by the tens place, hundreds place, thousands place, and so on, each increasing by a factor of 10. For example:

**The number “1234” can be broken down as follows:**

4 is in the units place and represents 4 ones.

3 is in the tens place and represents 3 tens.

2 is in the hundreds place and represents 2 hundreds.

1 is in the thousands place and represents 1 thousand.

### Decimal Point

The decimal point is used to separate the ones place from the tenths place in decimals. (It is also used to separate dollars from cents in money.) As we move to the right of the decimal point, each number place is divided by 10.

The number “123.456” can be broken down as follows:

4 is in the units place, representing 4 ones.

5 is in the tenths place, representing 5 tenths.

6 is in the hundredths place, representing 6 hundredths.

3 is in the thousands place, representing 3 thousands.

2 is in the ten-thousands place, representing 2 ten-thousands.

1 is in the hundred-thousands place, representing 1 hundred-thousand.

## Examples

### a. Whole Number

Example 1: The number “42” is a decimal number. It has no fractional part, so it’s considered a whole number. In this case, 4 is in the tens place, representing 4 tens, and 2 is in the units place, representing 2 ones.

### b. Decimal Fraction

Example 2: The number “0.75” is a decimal number. The decimal point separates the whole part (0) from the fractional part (75). Here, 7 is in the tenths place, representing 7 tenths, and 5 is in the hundredths place, representing 5 hundredths.

### c. Mixed Number

Example 3: The number “3.25” is a mixed decimal number. The whole part is 3, and the decimal part is 0.25. In this case, 3 is in the units place, representing 3 ones, 2 is in the tenths place, representing 2 tenths, and 5 is in the hundredths place, representing 5 hundredths.

Decimals provide a flexible way to represent both whole numbers and fractional parts, making them a fundamental part of mathematics and everyday life