Page 50 - Start Up Mathematics_7

3 Decimals

Sometimes, numbers do not appear as whole numbers or fractions. Instead, they appear in the
form of decimal numbers as 287.86. The ‘.’ in the decimal number is called the decimal point.
The numbers expressed in decimal form are also known as decimals.
We have learnt about decimal numbers in our previous classes. Let’s have a look at the following
place value table to recall what we have studied:

LAKHS THOUSANDS ONES

Ten Lakh Lakh Ten Thousand Thousand Hundred Ten One One-Tenth One- Hundredth One- Thousandth

1 1 1
10,00,000 1,00,000 10,000 1,000 100 10 1
10 100 1,000
Let’s write the number in the decimal form, given its place value expansion.

1 1
The number 8 × 100 + 5 × 10 + 7 × 1 + 4 × 10 + 6 × 100 in its decimal form is shown in
the following place value table.

Number in
Hundreds Tens Ones One-Tenths One-Hundredths
Decimal Form
8 5 7 4 6 857.46
The number 857.46 is read as eight hundred fifty-seven point four six.

Expanded Form of Decimals
Now let’s do the reverse, i.e., given a decimal number, let’s write it in expanded form.
1 1 1
7,468.205 = 7 × 1,000 + 4 × 100 + 6 × 10 + 8 × 1 + 2 × + 0 × + 5 ×
10 100 1,000
Example 1: Write the following decimal numbers in the expanded form:
(a) 5.23 (b) 500.03 (c) 5.734

1 1
Solution: (a) Expanded form of 5.23 = 5 × 1 + 2 × + 3 ×
10 100
1
(b) Expanded form of 500.03 = 5 × 100 + 3 × 100

(c) Expanded form of 5.734 = 5 × 1 + 7 × 1 + 3 × 1 + 4 × 1
10 100 1,000
Example 2: Write the place value of 2 in the following decimal numbers:
(a) 32.56 (b) 23.87 (c) 10.24 (d) 71.112