Decimal Place Value Notes & Questions | Class 5 Mathematics | Drishti OS

Decimal Place Value

What you'll learn

How decimal notation extends the Indian place-value system to tenths, hundredths, and thousandths after the decimal point.
To read and write decimals in money (₹ and paise) and measurement (metres, centimetres, kilograms).
To express decimals in expanded form and compare digit values by place.
To link decimals with fractions — especially tenths and hundredths from NCERT Math-Magic 5, Chapter 10 (Tenths and Hundredths).

Key concepts

Level 1 — Place value after the decimal point

Verbal: Each digit after the decimal point has a place value ten times smaller than the digit to its left.

Symbolic: In 6.408 → 6 ones, 4 tenths (0.4), 0 hundredths, 8 thousandths (0.008).

Place	Value	Fraction form	Example digit in 6.408
Ones	1	—	6
Tenths	1/10 = 0.1	1/10	4 → 0.4
Hundredths	1/100 = 0.01	1/100	0 → 0.00
Thousandths	1/1000 = 0.001	1/1000	8 → 0.008

NCERT link (Math-Magic 5, Ch 10): Price tags like ₹45.75 and lengths like 1.7 m appear throughout Tenths and Hundredths.

Level 2 — Money, expanded form, and trailing zeros

Verbal: 100 paise = ₹1, so 50 paise = ₹0.50 = fifty hundredths of a rupee.

Symbolic: ₹12.50 = 12 + 0.5 = 12 + 50/100; 2.34 = 2 + 0.3 + 0.04.

Representation	Meaning
₹45.75	45 rupees + 75 paise
0.6 = 0.60	Trailing zero does not change value
4.07	Zero holds the hundredths place — not 4.7

Real-life: A notebook costs ₹35.00; a pen ₹12.50; total ₹47.50 — read each place before paying.

Worked example

Read ₹127.05 and write it in expanded decimal form.

Step 1 — Whole part: 127 rupees.
Step 2 — Decimal part: 0.05 = 0 tenths + 5 hundredths = 5 paise.
Step 3 — Expanded: 100 + 20 + 7 + 0 + 0.05.
Answer: One hundred twenty-seven rupees and five paise.

In 6.408, which digit is in the hundredths place?

Step 1 — After decimal: 4 = tenths, 0 = hundredths, 8 = thousandths.
Answer: The digit 0 is in the hundredths place (value 0.00).

Common mistakes

Mistake	Why it happens	Fix
0.7 and 0.07 are the same	Ignoring place value	0.7 = 7 tenths; 0.07 = 7 hundredths — very different
Writing 4.7 for "four and seven hundredths"	Dropping the zero placeholder	Write 4.07 — zero keeps hundredths position
More decimal digits → always larger	Counting digits, not place value	Compare from left; 0.9 > 0.099
₹12.5 read as twelve rupees five paise	Missing trailing zero meaning	₹12.50 = 12 rupees 50 paise

Quick check

Write nine hundredths as a decimal. (0.09)
Express 3 + 0.2 + 0.05 as one decimal. (3.25)
In 8.306, what is the value of the digit 3? (3 tenths = 0.3)
Which is greater: 0.6 or 0.59? Explain using place value.
Stretch: ₹100 − ₹45.75 = ? Write the answer in rupees and paise. (₹54.25)

Revision tip: Draw a place-value chart with columns Ones · Tenths · Hundredths · Thousandths. Write three price tags from your home (₹) and label each digit's value.

Open the Practice tab for graded questions on Decimal Place Value.

Decimal Place Value