Learning Objectives
Let Us Begin!

Suresh goes to a shop in Delhi and buys a pencil for Rs 5.50. His mother gives him a Rs 10 note. The shopkeeper returns Rs 4.50. What does the dot (.) in Rs 5.50 mean?

The dot is called a decimal point. The number before the dot shows whole rupees (5 rupees), and the number after the dot shows paise (50 paise). Decimals help us write numbers that are between two whole numbers.

Step-by-Step Explanation

What is a Decimal?

A decimal is a number that has a whole part and a fractional part, separated by a decimal point (.).

In the number 3.7, the whole part is 3 and the fractional part is 7 tenths.

Decimals and Fractions -- They Are Related!

When we divide 1 whole into 10 equal parts, each part is called one-tenth. We write it as 1/10 or 0.1.

When we divide 1 whole into 100 equal parts, each part is called one-hundredth. We write it as 1/100 or 0.01.

FractionDecimalWe Say
1/100.1One-tenth
3/100.3Three-tenths
7/100.7Seven-tenths
1/1000.01One-hundredth
25/1000.25Twenty-five hundredths

Think about it: Rs 1 = 100 paise. So 50 paise = 50/100 of a rupee = Rs 0.50. Can you write 75 paise as a decimal?

Place Value in Decimals

Let us look at the number 24.63:

TensOnes. (Decimal Point)TenthsHundredths
24.63

The digit 2 is in the tens place (value = 20). The digit 4 is in the ones place (value = 4). The digit 6 is in the tenths place (value = 6/10 = 0.6). The digit 3 is in the hundredths place (value = 3/100 = 0.03).

Reading Decimal Numbers

We read 24.63 as "twenty-four point six three" (not "twenty-four point sixty-three").

We read 7.5 as "seven point five." We read 0.08 as "zero point zero eight."

Think about it: How would you read 15.09? Say each digit after the decimal point separately.

Comparing Decimals

To compare decimals, first compare the whole number part. If they are the same, compare the tenths. If those are also the same, compare the hundredths.

Example: 3.8 and 3.5 -- whole parts are the same (3 = 3). Compare tenths: 8 > 5. So 3.8 > 3.5.

Key Words and Meanings
WordMeaning
DecimalA number with a whole part and a fractional part separated by a decimal point
Decimal pointThe dot (.) that separates the whole part from the fractional part
TenthsThe first place after the decimal point (1/10)
HundredthsThe second place after the decimal point (1/100)
Place valueThe value of a digit based on its position in the number
Examples
Example 1: Writing a Fraction as a Decimal

Write 4/10 as a decimal. Since 4/10 means 4 tenths, we write it as 0.4.

Write 35/100 as a decimal. Since 35/100 means 35 hundredths, we write it as 0.35.

Example 2: Place Value

In the number 18.47, what is the place value of 4?

The digit 4 is in the tenths place. Its value is 4/10 = 0.4.

Example 3: Comparing Decimals with Money

Asha has Rs 12.75 and Deepa has Rs 12.50. Who has more money?

Whole parts: 12 = 12. Tenths: 7 > 5. So Rs 12.75 > Rs 12.50. Asha has more money.

Key Points to Remember
Practice Questions

A. Fill in the Blanks

  1. The decimal point separates the part from the part.
  2. 3/10 written as a decimal is .
  3. In 9.26, the digit 6 is in the place.
  4. Rs 8.25 means 8 rupees and paise.
  5. 0.50 is the same as the fraction .

B. Multiple Choice Questions

  1. Which decimal is equal to 7/10?
    (a) 7.0(b) 0.7(c) 0.07(d) 70.0
  2. In 15.83, the place value of 8 is:
    (a) 8 ones(b) 8 tens(c) 8 tenths(d) 8 hundredths
  3. Which is greater: 4.6 or 4.09?
    (a) 4.09(b) 4.6(c) Both are equal(d) Cannot tell

C. Write as Decimals

  1. 6/10 =
  2. 9/100 =
  3. 45/100 =
  4. 2 and 3/10 =

D. Compare Using > , < or =

  1. 5.3 5.7
  2. 0.80 0.8
  3. 12.45 12.54
  4. 7.10 7.1

E. Short Answer

  1. Ramesh bought a book for Rs 45.75 and a pen for Rs 12.50. Write both amounts in words.
  2. Arrange in ascending order (smallest to largest): 3.9, 3.2, 3.7, 3.5
Think and Do -- Fun Activity

Decimal Shopping: Look at 5 items in your home (a packet of dal, a bottle of oil, a chocolate, etc.). Write down their prices. Identify the whole rupee part and the paise part for each.

ItemPrice (Rs)Whole RupeesPaise

Now arrange the prices from smallest to largest: _______________________________________________