What is the Value of a Decimal Digit?

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Grade Level:

Class 3

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

Definition

What is it?

The value of a decimal digit tells us how much that digit is worth based on its position after the decimal point. It shows whether the digit represents tenths, hundredths, thousandths, and so on. Understanding this helps us work with parts of whole numbers.

Simple Example

Quick Example

Imagine you bought a packet of biscuits for Rs 12.50. The '5' after the decimal point means 50 paise, which is 5 tenths of a rupee. If it was Rs 12.05, the '5' would mean 5 paise, which is 5 hundredths of a rupee. The digit '5' has a different value depending on its place.

Worked Example

Step-by-Step

Let's find the value of each digit in the decimal number 7.345.

---1. Identify the whole number part: The digit '7' is to the left of the decimal point, so its value is 7 ones, or just 7.

---2. Identify the first decimal place (tenths): The digit '3' is immediately after the decimal point. This means it is in the tenths place. So, its value is 3 tenths, which can be written as 0.3 or 3/10.

---3. Identify the second decimal place (hundredths): The digit '4' is in the second position after the decimal point. This means it is in the hundredths place. So, its value is 4 hundredths, which can be written as 0.04 or 4/100.

---4. Identify the third decimal place (thousandths): The digit '5' is in the third position after the decimal point. This means it is in the thousandths place. So, its value is 5 thousandths, which can be written as 0.005 or 5/1000.

Answer: In 7.345, the value of 7 is 7, the value of 3 is 0.3, the value of 4 is 0.04, and the value of 5 is 0.005.

Why It Matters

Understanding decimal digit values is crucial for careers in finance, data science, and engineering. From calculating interest on a bank loan to precisely measuring ingredients in a lab, decimals help us work with exact quantities. It's how we deal with money, measurements, and data every day.

Common Mistakes

MISTAKE: Thinking 0.2 and 0.02 have the same value. | CORRECTION: 0.2 means 2 tenths, while 0.02 means 2 hundredths. 2 tenths (0.2) is much larger than 2 hundredths (0.02), just like 20 paise is more than 2 paise.

MISTAKE: Confusing the place value with the digit itself. For example, saying the value of 5 in 0.5 is 'hundredths'. | CORRECTION: The place value is 'tenths', and the digit is '5'. So, the value of the digit 5 in the tenths place is 5 tenths, or 0.5.

MISTAKE: Not writing zeros as placeholders. For example, writing the value of 3 in 0.03 as 0.3. | CORRECTION: The zeros after the decimal point but before the digit are important placeholders. For 0.03, the 3 is in the hundredths place, so its value is 0.03. The first zero holds the tenths place.

Practice Questions

Try It Yourself

QUESTION: What is the value of the digit '6' in the number 15.62? | ANSWER: 0.6

QUESTION: In the number 203.078, what is the value of the digit '7'? Write it as a decimal. | ANSWER: 0.07

QUESTION: A tailor measures a cloth piece as 5.405 meters. What is the value of the digit '5' in the thousandths place? | ANSWER: 0.005

MCQ

Quick Quiz

Which digit has a value of 0.09 in the number 4.192?

The Correct Answer Is:

The digit '9' is in the second place after the decimal point, which is the hundredths place. So, its value is 9 hundredths, or 0.09. The other options are in different place values.

Real World Connection

In the Real World

When you check your mobile data usage, it might show 1.5 GB used. Here, the '5' after the decimal means 5 tenths of a GB, or 500 MB. Similarly, when a cricketer scores 50.5 runs (not common but possible in averages), the '5' means half a run. Even your electricity bill might have decimal units, where understanding the value helps you verify calculations.

Key Vocabulary

Key Terms

DECIMAL POINT: The dot separating the whole number part from the fractional part of a number. | TENTHS: The first place value after the decimal point, meaning one part out of ten. | HUNDREDTHS: The second place value after the decimal point, meaning one part out of one hundred. | THOUSANDTHS: The third place value after the decimal point, meaning one part out of one thousand. | PLACE VALUE: The position of a digit in a number that determines its value.

What's Next

What to Learn Next

Now that you understand the value of individual decimal digits, you're ready to learn about comparing and ordering decimals. This will help you decide which decimal number is bigger or smaller, which is super useful for shopping or ranking things!