What is the Value of Each Decimal Place?

S1-SA2-0365

Grade Level:

Class 3

All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry

Definition

What is it?

The value of each decimal place tells us how much a digit contributes to the total number after the decimal point. It shows whether a digit represents tenths, hundredths, thousandths, and so on, making the number more precise.

Simple Example

Quick Example

Imagine you are buying chai. If a cup costs ₹15.50, the '5' after the decimal point means 50 paise (half a rupee). It's not ₹5, but 50 paise, which is 5 tenths of a rupee. This small part makes a difference to the total cost!

Worked Example

Step-by-Step

Let's find the value of each digit in the number 23.456

Step 1: Identify the whole number part and the decimal part.
Whole number part: 23
Decimal part: .456

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Step 2: Find the value of digits in the whole number part.
'2' is in the tens place, so its value is 2 x 10 = 20.
'3' is in the ones place, so its value is 1 x 3 = 3.

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Step 3: Find the value of digits in the decimal part.
The first digit after the decimal point is '4'. It's in the tenths place.
Its value is 4 x (1/10) = 4/10 = 0.4

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Step 4: The second digit after the decimal point is '5'. It's in the hundredths place.
Its value is 5 x (1/100) = 5/100 = 0.05

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Step 5: The third digit after the decimal point is '6'. It's in the thousandths place.
Its value is 6 x (1/1000) = 6/1000 = 0.006

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Answer: In 23.456, the values are: 20, 3, 0.4, 0.05, and 0.006.

Why It Matters

Understanding decimal place values is crucial for precision in many fields. From calculating exact finances in banking to measuring ingredients precisely in chemistry, or even coding AI models that need accurate data, this concept is fundamental. It helps engineers build accurate structures and scientists conduct precise experiments.

Common Mistakes

MISTAKE: Thinking 0.3 is larger than 0.35 because 3 is less than 35. | CORRECTION: Compare digits from left to right. 0.3 is 3 tenths, while 0.35 is 3 tenths and 5 hundredths, making 0.35 larger.

MISTAKE: Confusing the tenths place with the tens place. | CORRECTION: The tens place is before the decimal point (e.g., in 20.5, '2' is tens). The tenths place is immediately after the decimal point (e.g., in 20.5, '5' is tenths).

MISTAKE: Reading 0.12 as 'zero point twelve'. | CORRECTION: Read each digit after the decimal separately. So, 0.12 should be read as 'zero point one two', meaning one tenth and two hundredths.

Practice Questions

Try It Yourself

QUESTION: What is the value of the digit '7' in the number 12.75? | ANSWER: 0.7 (or 7 tenths)

QUESTION: In the number 0.039, which digit is in the hundredths place, and what is its value? | ANSWER: The digit '3' is in the hundredths place. Its value is 0.03.

QUESTION: A tailor measures a fabric as 2.405 meters. What is the value of the digit '5' in this measurement? Why is this precision important? | ANSWER: The value of '5' is 0.005 meters (or 5 thousandths of a meter). This precision is important for tailoring to ensure clothes fit perfectly and avoid wasting expensive fabric.

MCQ

Quick Quiz

Which of the following represents the smallest value?

0.5

0.05

0.5

0.005

The Correct Answer Is:

0.005 represents 5 thousandths, which is smaller than 5 tenths (0.5), 5 hundredths (0.05), or 50 hundredths (0.50). Adding zeros at the end of a decimal does not change its value (0.5 = 0.50).

Real World Connection

In the Real World

When you check the fuel price at a petrol pump, you often see prices like ₹108.45 per litre. The '45' after the decimal point tells you the cost in paise. Understanding these decimal places helps you know the exact amount you are paying, which is vital in everyday transactions and even for online payments like UPI.

Key Vocabulary

Key Terms

DECIMAL POINT: A dot that separates the whole number part from the fractional part of a number. | TENTHS PLACE: The first digit after the decimal point, representing parts out of ten. | HUNDREDTHS PLACE: The second digit after the decimal point, representing parts out of one hundred. | THOUSANDTHS PLACE: The third digit after the decimal point, representing parts out of one thousand.

What's Next

What to Learn Next

Great job understanding decimal place values! Next, you can explore 'Comparing and Ordering Decimals' or 'Adding and Subtracting Decimals'. These concepts build directly on knowing the value of each place, making calculations much easier.