Decimals

The numbers expressed in decimal form are called decimal numbers or simply decimals. For example – each of the numbers 5.8, 19.63, 7.295, 0.068 etc. is a decimal.

A decimal has two parts, namely

1. whole number part
2. decimal part

These parts are separated by a dot(.) called the decimal point. The part on the left side of the decimal point is called the whole number part and that on the right side of the decimal point is the decimal part.

Example: In 68.49, we have whole number part =68 and decimal part = 49.

Decimal Places: The number of digits contained in the decimal part of a decimal gives the number of decimal places. For example – 4.93 has two decimal places and 7.632 has three decimal places.

LIKE AND UNLIKE DECIMALS

LIKE DECIMALS: The decimals having the same number of decimal places are called like decimals. For example – 9.82, 6.03, 14.58 are like decimals, each having two decimal places.

UNLIKE DECIMALS: Decimals having a different number of decimal places are called, unlike decimals. For example – 6.4, 8.93 and 12.065 are unlike decimals.

NOTE: Putting any number of zeros to the extreme right of the decimal part of a decimal does not change its value.

PLACE VALUE CHART IN DECIMALS

• Zeroes on the left of a whole number have no value. For example 08, 008 is same as 8 or 8.
• Zeroes on the right side of the decimal number have no value. For example, 0.05 can also be written as 0.050 or 0.0500.

CONVERSION OF DECIMALS INTO FRACTION

e.g 

CONVERSION OF FRACTIONS INTO DECIMALS

e.g. latex]\frac{5953}{1000} = 5953[/latex]

ADDITION OF DECIMALS FRACTIONS

e.g. add 13.279, 3.00046 and 742.000372

ANS:

$$\begin{gathered} 13.279 \to 13.279000 \\ + 3.00046 \to + 3.000460 \\ +742.000372 \to +742.000372 \end{gathered}$$

SUBTRACTION OF DECIMAL FRACTION

e.g. Find 0.01 – 0.009 = ?

ANS:

$$\begin{gathered} 0.01 \to 0.010 \\ –0.009 \to –0.009 \end{gathered}$$