Understand Decimal Place Value: Simple Guide for Students

The concept of Place Value With Decimals is crucial in mathematics, helping students understand the true worth of a digit based on its position relative to the decimal point. This topic is tested in school exams and is essential for daily tasks like dealing with money, measurements, and data in science and technology.

Understanding Place Value With Decimals

Place value with decimals means every digit has a value based on where it sits in the number. Digits to the left of the decimal point represent whole numbers (ones, tens, hundreds, etc.), while digits to the right represent fractional parts (tenths, hundredths, thousandths, and so on). This system allows us to express numbers smaller than one and is fundamental in reading, writing, and comparing decimals.

Decimal Place Value Chart & How It Works

A decimal place value chart helps you quickly find the value of each digit in a number. The columns to the left of the decimal show units like ones and tens, while those to the right show tenths, hundredths, and beyond. For example, in 47.82, 7 is in the ones place, 8 is in the tenths place, and 2 is in the hundredths place.

To remember the order: Ones (1), tenths (0.1), hundredths (0.01), thousandths (0.001), and so on. Each step right is one-tenth the place just before it.

Reading and Writing Decimal Numbers

To read decimals, say the whole number part as usual, then read the digits after the decimal point followed by the place name. For example:

• 3.4 — "three and four tenths"
• 5.08 — "five and eight hundredths"
• 0.725 — "seven hundred twenty-five thousandths"

In written form, each digit has a different value based on its place. Let's expand 2.54:

2.54 = 2 (ones) + 5 (tenths, 0.5) + 4 (hundredths, 0.04)

Formulae and Digital Representation

There isn't a direct formula but place value can be represented as:

Number = (Whole part) + (First decimal digit × 1/10) + (Second decimal digit × 1/100) + (Third decimal digit × 1/1000) + …

For instance, 7.206 can be written as 7 + 2/10 + 0/100 + 6/1000

Worked Examples

Example 1

Write the place value of each digit in 4.523:

1. 4 is in the ones place — its value = 4 × 1 = 4
2. 5 is in the tenths place — its value = 5 × 0.1 = 0.5
3. 2 is in the hundredths place — its value = 2 × 0.01 = 0.02
4. 3 is in the thousandths place — its value = 3 × 0.001 = 0.003

Example 2

Express 0.76 in expanded form:

• 0.7 (tenths)
• 0.06 (hundredths)

So, 0.76 = 7/10 + 6/100

Example 3

In 15.408, what is the place value of 8?

8 is in the thousandths place, so its value is 0.008 or 8/1000.

Practice Problems

• Write the place value of 5 in 84.359.
• Expand the number 6.09 using place values.
• What digit is in the hundredths place in 7.428?
• Reading: How is 12.407 said in words?
• Write 9.005 in expanded form.

Common Mistakes to Avoid

• Confusing tenths with tens (0.1 vs. 10).
• Forgetting a zero placeholder (e.g., 0.504 is not equal to 0.54).
• Reading digits instead of values (e.g., reading 0.32 as “zero point thirty-two” instead of “thirty-two hundredths”).
• Ignoring the decimal point's effect on place value.

Real-World Applications

Place value with decimals is used every day:

• Money: ₹45.75 — 45 rupees and 75 paise; the 7 is worth 0.7 rupees (70 paise).
• Measurements: A length of 2.35 m means 2 meters and 35 centimeters (since 0.01 m = 1 cm).
• Science: Water boils at 100.00°C; precision to the hundredths place matters in experiments.

At Vedantu, we show how understanding decimal place value helps you confidently solve real-life problems and ace exam questions.

Page Summary

In this lesson, we explored Place Value With Decimals, learned to recognize each digit's value based on its position, and saw both expanded forms and real-world examples. Understanding decimal place value will help you read, write, and compare decimal numbers accurately in maths and daily life. For further practice, check out these essential topics:

• Decimal Number System
• Place Value (Whole Numbers)
• Converting Fractions into Decimals
• Decimal Expansion of Rational Numbers
• Expanded Form of Decimals and Place Value
• Ordering Decimals

Keep practicing with Vedantu to master decimal place value and boost your confidence in mathematics!