What is Place Value in Decimals?

S1-SA2-0253

Grade Level:

Class 4

Maths, Finance, Computing, AI

Definition

What is it?

Place value in decimals tells us the value of each digit based on its position after the decimal point. Just like whole numbers have ones, tens, hundreds, decimals have tenths, hundredths, and thousandths to show parts of a whole.

Simple Example

Quick Example

Imagine you buy a small packet of biscuits for Rs. 15.50. Here, the '1' is in the tens place (Rs. 10), the '5' before the decimal is in the ones place (Rs. 5), the '5' after the decimal is in the tenths place (50 paise or 0.50 rupees), and the '0' is in the hundredths place (meaning no additional hundredths of a rupee).

Worked Example

Step-by-Step

Let's find the place value of each digit in the number 24.375.

Step 1: Identify the whole number part and the decimal part. The whole number part is 24, and the decimal part is 375.

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Step 2: For the whole number part, assign place values as usual. '2' is in the tens place, so its value is 2 x 10 = 20. '4' is in the ones place, so its value is 4 x 1 = 4.

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Step 3: For the decimal part, start immediately after the decimal point. The first digit '3' is in the tenths place. Its value is 3 x (1/10) or 3 x 0.1 = 0.3.

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Step 4: The second digit '7' is in the hundredths place. Its value is 7 x (1/100) or 7 x 0.01 = 0.07.

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Step 5: The third digit '5' is in the thousandths place. Its value is 5 x (1/1000) or 5 x 0.001 = 0.005.

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Answer: In 24.375, the place value of 2 is 20, 4 is 4, 3 is 0.3, 7 is 0.07, and 5 is 0.005.

Why It Matters

Understanding decimal place value is crucial for handling money accurately, like when calculating chai prices or mobile data usage. It's fundamental in fields like finance for banking and investments, and in computing for precise measurements. Engineers and scientists use it daily for accurate calculations.

Common Mistakes

MISTAKE: Confusing tenths with tens, or hundredths with hundreds. For example, thinking the '3' in 0.3 means 30. | CORRECTION: Remember 'ths' at the end means it's a part of a whole, so tenths (1/10) is much smaller than tens (10).

MISTAKE: Starting place value counting from the right for decimals, similar to whole numbers. For example, calling the '7' in 0.37 the tenths place. | CORRECTION: For decimals, place value starts immediately to the RIGHT of the decimal point with tenths, then hundredths, then thousandths.

MISTAKE: Ignoring trailing zeros in decimals when writing place values. For example, saying 0.50 has the '0' in the hundredths place but not assigning it a value. | CORRECTION: Every digit, including zero, holds a place value. In 0.50, the 0 is in the hundredths place, meaning there are 'zero hundredths'.

Practice Questions

Try It Yourself

QUESTION: What is the place value of the digit '6' in the number 12.65? | ANSWER: The '6' is in the tenths place, so its value is 0.6.

QUESTION: Write the number 300 + 4 + 0.2 + 0.08 in standard decimal form. | ANSWER: 304.28

QUESTION: In a cricket match, a player scored 87.25 runs. What is the value of the digit '2' in this score? What about the digit '5'? | ANSWER: The value of '2' is 0.2 (tenths place). The value of '5' is 0.05 (hundredths place).

MCQ

Quick Quiz

Which digit is in the hundredths place in the number 543.192?

The Correct Answer Is:

The digit '1' is in the tenths place, '9' is in the hundredths place, and '2' is in the thousandths place. The digits before the decimal are whole number place values.

Real World Connection

In the Real World

When you check your mobile data usage, you might see 1.75 GB remaining. Here, '1' is the whole GB, '7' is 7 tenths of a GB (0.7 GB), and '5' is 5 hundredths of a GB (0.05 GB). This helps you understand exactly how much data you have left.

Key Vocabulary

Key Terms

DECIMAL POINT: The dot that separates the whole number part from the fractional part of a number | TENTHS: The first place value to the right of the decimal point, representing 1/10 of a whole | HUNDREDTHS: The second place value to the right of the decimal point, representing 1/100 of a whole | THOUSANDTHS: The third place value to the right of the decimal point, representing 1/1000 of a whole | PLACE VALUE: The value of a digit based on its position in a number.

What's Next

What to Learn Next

Great job understanding decimal place value! Next, you should learn about 'Comparing Decimals'. This will build on your knowledge of place value to help you decide which decimal number is larger or smaller, which is very useful for shopping or measurements.