Decimal Place Value (Grade 5)

Q: What are the decimal places called?

The first place after the decimal point is tenths (1/10), the second is hundredths (1/100), and the third is thousandths (1/1000). These continue as ten-thousandths, hundred-thousandths, etc.

Q: Does adding a zero at the end of a decimal change its value?

No. Adding trailing zeroes after the last decimal digit does not change the value. 3.5 = 3.50 = 3.500. However, zeroes between the decimal point and a digit do matter: 3.05 is not the same as 3.5.

Q: How do I compare two decimal numbers?

Compare digit by digit from left to right. First compare the whole number parts, then tenths, then hundredths, and so on. Make the decimal places equal by adding trailing zeroes if needed.

Q: How is decimal place value related to fractions?

Tenths = 1/10, hundredths = 1/100, thousandths = 1/1000. So 0.3 = 3/10, 0.07 = 7/100, 0.005 = 5/1000. Decimals are just another way of writing fractions with denominators that are powers of 10.

Q: What is the difference between 0.4 and 0.04?

0.4 = 4 tenths = 4/10, while 0.04 = 4 hundredths = 4/100. The value of 0.4 is 10 times greater than 0.04. The position of the digit relative to the decimal point determines its value.

Q: How does place value help with money?

In Indian currency, ₹45.75 means 45 rupees and 75 paise. The tenths digit (7) represents 70 paise, and the hundredths digit (5) represents 5 paise. Understanding decimal place value prevents errors in money calculations.

Q: How do I write the expanded form of a decimal?

Write each digit multiplied by its place value. For 23.45: 20 + 3 + 0.4 + 0.05, or equivalently 2×10 + 3×1 + 4×(1/10) + 5×(1/100).

Q: Can a decimal number have a zero in the tenths place?

Yes. For example, 5.08 has 0 in the tenths place and 8 in the hundredths place. This means there are no tenths, but there are 8 hundredths. The 0 acts as a placeholder and cannot be removed.

Class 5Decimals (Grade 5)

In Class 5, students deepen their understanding of decimal place value by working with tenths, hundredths, and thousandths. Just as whole numbers have places (ones, tens, hundreds), decimal numbers have places to the right of the decimal point that represent parts smaller than 1.

Decimal place value is essential for working with money (₹45.75 means 45 rupees and 75 paise), measurements (1.5 metres), and scientific data.

What is Decimal Place Value - Class 5 Maths (Decimals)?

The decimal point separates the whole number part from the fractional part. Each place to the right of the decimal point is 1/10 of the place to its left.

Tens	Ones	.	Tenths	Hundredths	Thousandths
10	1	.	1/10 = 0.1	1/100 = 0.01	1/1000 = 0.001

Example: In 34.567:

3 is in the tens place → value = 30
4 is in the ones place → value = 4
5 is in the tenths place → value = 5/10 = 0.5
6 is in the hundredths place → value = 6/100 = 0.06
7 is in the thousandths place → value = 7/1000 = 0.007

Decimal Place Value (Grade 5) Formula

Place Value of a decimal digit = Digit × Value of its place

Tenths = 1/10 | Hundredths = 1/100 | Thousandths = 1/1000

Solved Examples

Example 1: Example 1: Identifying place values

Problem: Write the place value of each digit in 25.347.

Solution:

2 → Tens → 20
5 → Ones → 5
3 → Tenths → 3/10 = 0.3
4 → Hundredths → 4/100 = 0.04
7 → Thousandths → 7/1000 = 0.007

Example 2: Example 2: Expanded form of a decimal

Problem: Write 18.265 in expanded form.

Solution:

18.265 = 10 + 8 + 2/10 + 6/100 + 5/1000

= 10 + 8 + 0.2 + 0.06 + 0.005

Answer: 10 + 8 + 0.2 + 0.06 + 0.005

Example 3: Example 3: Writing a decimal from expanded form

Problem: Write in standard form: 40 + 3 + 0.5 + 0.08 + 0.002.

Solution:

40 + 3 = 43; 0.5 + 0.08 + 0.002 = 0.582

Answer: 43.582

Example 4: Example 4: Place value vs face value

Problem: In 7.639, find the place value and face value of 3.

Solution:

The digit 3 is in the hundredths place.

Face value: 3

Place value: 3 × 1/100 = 3/100 = 0.03

Example 5: Example 5: Comparing using place value

Problem: Which is greater: 4.35 or 4.305?

Solution:

Step 1: Ones: 4 = 4

Step 2: Tenths: 3 = 3

Step 3: Hundredths: 5 > 0

Answer: 4.35 > 4.305

Example 6: Example 6: Converting fraction to decimal using place value

Problem: Express 7/1000 as a decimal.

Solution:

7/1000 means 7 in the thousandths place.

Answer: 7/1000 = 0.007

Example 7: Example 7: Word problem — Money

Problem: Ria has ₹56.85. What is the value of the digit 8 in this amount?

Solution:

In ₹56.85, the digit 8 is in the tenths place.

Value = 8 tenths = 8/10 = ₹0.80 = 80 paise.

Answer: The digit 8 represents 80 paise (₹0.80).

Example 8: Example 8: Ordering decimals by place value

Problem: Arrange in ascending order: 3.14, 3.104, 3.141, 3.1.

Solution:

Write with equal decimal places: 3.140, 3.104, 3.141, 3.100

Compare: 3.100 < 3.104 < 3.140 < 3.141

Answer: 3.1, 3.104, 3.14, 3.141

Example 9: Example 9: Writing a decimal number on a place value chart

Problem: Place 609.052 on a place value chart.

Solution:

H	T	O	.	Tenths	Hundredths	Thousandths
6	0	9	.	0	5	2

Key Points to Remember

The decimal point separates whole number places (left) from fractional places (right).
Tenths = 1/10, Hundredths = 1/100, Thousandths = 1/1000.
Each place to the right is 1/10 of the place to its left.
Adding trailing zeroes after the last decimal digit does not change the value (3.5 = 3.50 = 3.500).
To compare decimals, compare digit by digit from left to right, starting at the highest place.
The place value of a digit = digit × value of its position.
The face value of a digit is just the digit itself, regardless of position.

Practice Problems

Write the place value of 6 in 42.618.
Write 75.034 in expanded form.
Write in standard form: 200 + 9 + 0.4 + 0.003.
Arrange in descending order: 5.67, 5.607, 5.076, 5.670.
In ₹123.45, what is the value of each digit after the decimal point?
Express 23/1000 as a decimal.
Which is greater: 0.52 or 0.502? Explain using place value.
Write 8.009 on a place value chart.

Frequently Asked Questions

Q1. What are the decimal places called?

The first place after the decimal point is tenths (1/10), the second is hundredths (1/100), and the third is thousandths (1/1000). These continue as ten-thousandths, hundred-thousandths, etc.

Q2. Does adding a zero at the end of a decimal change its value?

No. Adding trailing zeroes after the last decimal digit does not change the value. 3.5 = 3.50 = 3.500. However, zeroes between the decimal point and a digit do matter: 3.05 is not the same as 3.5.

Q3. How do I compare two decimal numbers?

Compare digit by digit from left to right. First compare the whole number parts, then tenths, then hundredths, and so on. Make the decimal places equal by adding trailing zeroes if needed.

Q4. How is decimal place value related to fractions?

Tenths = 1/10, hundredths = 1/100, thousandths = 1/1000. So 0.3 = 3/10, 0.07 = 7/100, 0.005 = 5/1000. Decimals are just another way of writing fractions with denominators that are powers of 10.

Q5. What is the difference between 0.4 and 0.04?

0.4 = 4 tenths = 4/10, while 0.04 = 4 hundredths = 4/100. The value of 0.4 is 10 times greater than 0.04. The position of the digit relative to the decimal point determines its value.

Q6. How does place value help with money?

In Indian currency, ₹45.75 means 45 rupees and 75 paise. The tenths digit (7) represents 70 paise, and the hundredths digit (5) represents 5 paise. Understanding decimal place value prevents errors in money calculations.

Q7. How do I write the expanded form of a decimal?

Write each digit multiplied by its place value. For 23.45: 20 + 3 + 0.4 + 0.05, or equivalently 2×10 + 3×1 + 4×(1/10) + 5×(1/100).

Q8. Can a decimal number have a zero in the tenths place?

Yes. For example, 5.08 has 0 in the tenths place and 8 in the hundredths place. This means there are no tenths, but there are 8 hundredths. The 0 acts as a placeholder and cannot be removed.

Decimal Place Value (Grade 5)

What is Decimal Place Value - Class 5 Maths (Decimals)?

Decimal Place Value (Grade 5) Formula

Solved Examples

Example 1: Example 1: Identifying place values

Example 2: Example 2: Expanded form of a decimal

Example 3: Example 3: Writing a decimal from expanded form

Example 4: Example 4: Place value vs face value

Example 5: Example 5: Comparing using place value

Example 6: Example 6: Converting fraction to decimal using place value

Example 7: Example 7: Word problem — Money

Example 8: Example 8: Ordering decimals by place value

Example 9: Example 9: Writing a decimal number on a place value chart

Key Points to Remember

Practice Problems

Frequently Asked Questions

Q1. What are the decimal places called?

Q2. Does adding a zero at the end of a decimal change its value?

Q3. How do I compare two decimal numbers?

Q4. How is decimal place value related to fractions?

Q5. What is the difference between 0.4 and 0.04?

Q6. How does place value help with money?

Q7. How do I write the expanded form of a decimal?

Q8. Can a decimal number have a zero in the tenths place?

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