Place Value Chart for Decimals with Examples and Step by Step Explanation
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.
| Place | Value | Example (5.348) |
|---|---|---|
| Ones | 1 | 5 |
| Tenths | 0.1 | 3 |
| Hundredths | 0.01 | 4 |
| Thousandths | 0.001 | 8 |
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.
| Thousands | Hundreds | Tens | Ones | Decimal Point | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|---|
| 4 | 7 | 9 | 5 | . | 2 | 8 | 1 |
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:
- 4 is in the ones place — its value = 4 × 1 = 4
- 5 is in the tenths place — its value = 5 × 0.1 = 0.5
- 2 is in the hundredths place — its value = 2 × 0.01 = 0.02
- 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)
- 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!
FAQs on Understanding Place Value With Decimals in Maths
1. What is place value with decimals?
Place value with decimals is the value of each digit based on its position to the left or right of the decimal point. In a decimal number:
- Digits to the left represent whole numbers (ones, tens, hundreds).
- Digits to the right represent parts of a whole (tenths, hundredths, thousandths).
- For example, in 4.582:
- 4 is in the ones place.
- 5 is in the tenths place.
- 8 is in the hundredths place.
- 2 is in the thousandths place.
2. What are the place values to the right of the decimal point?
The place values to the right of the decimal point are tenths, hundredths, thousandths, and so on. Each place is 10 times smaller than the one to its left.
- 1st place: Tenths (1/10)
- 2nd place: Hundredths (1/100)
- 3rd place: Thousandths (1/1000)
- 4th place: Ten-thousandths (1/10,000)
3. How do you read decimal numbers using place value?
You read a decimal number by saying the whole number part, saying “point,” then reading each digit after the decimal separately. For example, 3.45 is read as “three point four five.”
- Say the whole number before the decimal.
- Say “point” for the decimal point.
- Read each digit to the right individually.
4. How do you write decimals in expanded form?
To write decimals in expanded form, multiply each digit by its place value and add the results. For example, 6.203 in expanded form is:
- 6 × 1 = 6
- 2 × 0.1 = 0.2
- 0 × 0.01 = 0
- 3 × 0.001 = 0.003
5. How do you find the value of a digit in a decimal number?
To find the value of a digit in a decimal number, multiply the digit by its place value. For example, in 8.76:
- The 7 is in the tenths place, so its value is 7 × 0.1 = 0.7.
- The 6 is in the hundredths place, so its value is 6 × 0.01 = 0.06.
6. How do you compare decimals using place value?
To compare decimals, line up the decimal points and compare digits from left to right by place value. Follow these steps:
- Write the numbers vertically with decimal points aligned.
- Add zeros if needed to make equal decimal places.
- Compare digits starting from the leftmost place.
- Write as 0.750 and 0.705.
- Since 750 thousandths > 705 thousandths, 0.75 is greater than 0.705.
7. What is the difference between tenths and hundredths?
The difference between tenths and hundredths is that tenths represent 1/10 while hundredths represent 1/100. A tenth is ten times larger than a hundredth.
- 1 tenth = 0.1
- 1 hundredth = 0.01
- 0.1 = 10 × 0.01
8. How do you round decimals using place value?
To round decimals, look at the digit to the right of the rounding place and apply the rounding rule. Steps:
- Identify the place value you are rounding to.
- Check the digit to its right.
- If it is 5 or more, increase the rounding digit by 1.
- If it is less than 5, keep it the same.
- The thousandths digit is 6.
- Since 6 ≥ 5, round up.
- The result is 4.38.
9. How do trailing zeros affect decimal place value?
Trailing zeros to the right of a decimal do not change the value of the number. For example, 2.5 = 2.50 = 2.500.
- 2.5 means 2 and 5 tenths.
- 2.50 means 2 and 50 hundredths.
- Both represent the same quantity.
10. Can you give an example of place value in decimals?
An example of place value in decimals is the number 12.345, where each digit has a specific value based on its position.
- 1 is in the tens place (value 10).
- 2 is in the ones place (value 2).
- 3 is in the tenths place (value 0.3).
- 4 is in the hundredths place (value 0.04).
- 5 is in the thousandths place (value 0.005).
