What is Decimal Place Value?

S3-SA4-0071

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

Decimal place value tells us the value of each digit in a decimal number based on its position. It extends our understanding of whole number place value to include parts of a whole, represented after the decimal point.

Simple Example

Quick Example

Imagine you buy a packet of biscuits for Rs 25.50. The '2' is in the tens place, '5' is in the ones place. After the decimal point, the first '5' is in the tenths place (meaning 50 paise, or 50/100 of a rupee), and the '0' is in the hundredths place.

Worked Example

Step-by-Step

Let's find the place value of each digit in the number 143.67.

1. Start with the digits before the decimal point (whole numbers).
---2. The digit '3' is in the ones place, so its value is 3 x 1 = 3.
---3. The digit '4' is in the tens place, so its value is 4 x 10 = 40.
---4. The digit '1' is in the hundreds place, so its value is 1 x 100 = 100.
---5. Now, look at the digits after the decimal point.
---6. The digit '6' is in the tenths place, so its value is 6 x (1/10) = 0.6.
---7. The digit '7' is in the hundredths place, so its value is 7 x (1/100) = 0.07.
---Answer: The place values are: 100, 40, 3, 0.6, and 0.07.

Why It Matters

Understanding decimal place value is crucial for accuracy in many fields. Data scientists use it for precise calculations, engineers for designing structures, and economists for financial models. It helps ensure things like rocket launches, medical dosages, or bank transactions are perfectly accurate.

Common Mistakes

MISTAKE: Thinking the first digit after the decimal point is the 'ones' place. | CORRECTION: The first digit after the decimal point is the 'tenths' place.

MISTAKE: Confusing tenths with tens, and hundredths with hundreds. | CORRECTION: 'Tenths' (1/10) and 'hundredths' (1/100) are for parts of a whole, while 'tens' (10) and 'hundreds' (100) are for whole numbers.

MISTAKE: Not realizing that adding zeros at the end of a decimal number (like 0.5 becomes 0.500) doesn't change its value. | CORRECTION: Zeros at the end of the decimal part do not change the value of the number (e.g., 0.5 is the same as 0.50 or 0.500).

Practice Questions

Try It Yourself

QUESTION: What is the place value of the digit '9' in the number 5.92? | ANSWER: 0.9 (nine tenths)

QUESTION: Write the number 300 + 40 + 7 + 0.8 + 0.05 in standard decimal form. | ANSWER: 347.85

QUESTION: In the number 12.345, which digit is in the thousandths place? What is its value? | ANSWER: The digit '5' is in the thousandths place. Its value is 0.005.

MCQ

Quick Quiz

Which digit is in the hundredths place in the number 24.608?

The Correct Answer Is:

The hundredths place is the second digit after the decimal point. In 24.608, '6' is in the tenths place, and '0' is in the hundredths place.

Real World Connection

In the Real World

When you check your mobile data usage, it might show 1.5 GB remaining. Here, '1' is a whole GB, and '.5' means half a GB. Or, when a cricket commentator says a player scored at a strike rate of 145.7, they are using decimal place values to show the average runs per 100 balls, with '7' representing seven-tenths of a run.

Key Vocabulary

Key Terms

DECIMAL POINT: The dot that separates the whole number part from the fractional part of a number | TENTHS PLACE: The first digit after the decimal point, representing fractions of 10 | HUNDREDTHS PLACE: The second digit after the decimal point, representing fractions of 100 | THOUSANDTHS PLACE: The third digit after the decimal point, representing fractions of 1000 | PLACE VALUE: The value of a digit based on its position in a number

What's Next

What to Learn Next

Great job learning about decimal place value! Next, you should explore 'Comparing and Ordering Decimals'. This concept will help you understand which decimal number is larger or smaller, which is super useful in daily life and builds directly on knowing each digit's value.