Page 34 - Maths Skills - 7

32 Maths

DECIMAL FRACTIONS
The fractions with denominators 10, 100, 1000, etc. are known as decimal fractions.

9 8 65
For example; , and , etc. are decimal fractions.
10 100 1000
5
(i) A fraction whose denominator is 10, such as or 0.5, is known as a one-place decimal.
10
7
(ii) A fraction whose denominator is 100, such as or 0.07, is known as a two-place decimal.
100

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(iii) A fraction whose denominator is 1000, such as 1000 or 0.008, is known as a three-place decimal and
so on.

DECIMALS
The numbers that are expressed in decimal form are called decimal numbers or simply decimals.
For example; 6.5, 2.509, 0.005, etc. are decimals.
A decimal has two parts:

(i) whole number (ii) decimal

These two parts are separated by a dot (.) called the decimal point.
For example; 6.29 is read as six point two nine. Here, 6 is the whole number part and two nine is the decimal part.

LIKE DECIMALS AND UNLIKE DECIMALS

● Two or more decimals having the same number of decimal places are called like decimals.
For example; 6.32, 4.09, 16.73 and 112.29 are like decimals as they all have two decimal places.

● Two or more decimals having different number of decimal places are called unlike decimals.
For example; 0.4, 9.56, 3.065 are unlike decimals.

MULTIPLICATION OF DECIMALS
Rule for multiplying two decimals:

Step 1. Multiply the given decimals without taking the decimal point into consideration.
Step 2. Count the decimal places in multiplicand and the multiplier and find the sum of decimal places.

Step 3. Count from right the digits of the product equal to the sum obtained in Step 2 and put the decimal point
after those many digits from right.

Multiplication of a Decimal by 10, 100, 1000, …, etc.
To multiply a decimal number with 10, 100, 1000, 10000, etc, count the number of zeros following 1 in the
multiplier and shift the decimal point of multiplicand towards right for the places equal to the above count. Fill in
the vacant places if any, by 0s.
For example; 16.782 × 100 = 1678.2

Since there are two zeroes following 1 in 100, the decimal point in the product moves two places towards right.
Similarly, 115.72 × 10 = 1157.2 and 23.6785 × 1000 = 23678.5