Decimal place value is a concept in mathematics that helps us understand the value of each digit in a decimal number. It’s essential to grasp this concept when working with decimals, as it allows us to compare, add, subtract, multiply, and divide decimal numbers effectively.

In this article, we’ll explore decimal place value in detail, breaking down the concept step by step to make it easy for you to understand.

## What are Decimals?

Before we dive into decimal place value, let’s briefly discuss decimals. A decimal number is a number that has a whole part and a fractional part, separated by a decimal point.

For example, in the decimal number 12.34, the whole part is 12 and the fractional part is 34. Decimal numbers are a convenient way to represent fractions and real numbers that are not whole numbers.

## Decimal Place Value: The Basics

Every digit in a decimal number has a specific place value. Place value determines the value of a digit based on its position within the number. In a decimal number, we have the whole part on the left side of the decimal point and the fractional part on the right side.

### Whole Part Place Values

For the whole part, place values increase from right to left. Here are the basic place values for whole numbers:

- Ones (1)
- Tens (10)
- Hundreds (100)
- Thousands (1,000)
- Ten Thousands (10,000)
- Hundred Thousands (100,000)
- Millions (1,000,000)

…and so on.

### Fractional Part Place Values

For the fractional part, place values decrease from left to right. Here are the basic place values for decimal fractions:

- Tenths (0.1)
- Hundredths (0.01)
- Thousandths (0.001)
- Ten Thousandths (0.0001)
- Hundred Thousandths (0.00001)
- Millionths (0.000001)

…and so on.

## Identifying Decimal Place Values: Step by Step

Now that we understand the basic concept of decimal place values, let’s practice identifying them in a decimal number.

### Example: Find the place values of the digits in the decimal number 123.456.

**Step 1**: Identify the whole part and the fractional part.

Whole part: 123 Fractional part: 456

**Step 2**: Identify the place value of each digit in the whole part.

1: Hundreds (100) 2: Tens (10) 3: Ones (1)

**Step 3**: Identify the place value of each digit in the fractional part.

4: Tenths (0.1) 5: Hundredths (0.01) 6: Thousandths (0.001)

So, the place values of the digits in the decimal number 123.456 are:

1 → Hundreds (100) 2 → Tens (10) 3 → Ones (1) 4 → Tenths (0.1) 5 → Hundredths (0.01) 6 → Thousandths (0.001)

## Final Thoughts

Understanding decimal place value is essential when working with decimal numbers, as it helps us perform various arithmetic operations and compare decimal numbers accurately.

By breaking down the concept step by step and practicing identifying place values in different decimal numbers, you’ll become more comfortable and confident in your ability to work with decimals.

Remember, the key is to familiarize yourself with the basic place values for whole numbers and decimal fractions and apply this knowledge to any decimal number you encounter.