Chapter Notes and Summary
• Decimals : numbers expressed in decimal form are called decimal numbers or simply decimals. e.g. 2•5, 31•72, 8•391, 0•5, 0•01, 0•0003, etc. are decimals A decimal has two parts, namely : (i) whole-number part and (ii) decimal part.
These parts are separated by a dot (•) called decimal point.
e.g., 25•7512 Whole number part decimal and we can read its twenty five point seven five one two.
• Decimal fractions : fractions in which denominators are 10, 100, 1000 etc. are known as decimal fractions.
e.g., 3 10 7 100 35 1000 , , , etc. are all decimal fractions.
• Decimal Places : number of digits contained in decimal part of a decimal gives number of decimal places.
e.g., (i) 3•25 has two decimal places
(ii) 7•321 has three decimal places
• Like Decimals : Decimals having same number of decimal places are called like decimals.
e.g., 2•25, 11•03, 7•12,. 123•67 are like decimals
• Unlike Decimals : Decimals having different number of decimal places are called unlike decimals. e.g., 6•012, 12•1, 3•97, 1•0001 are unlike decimals
• Comparing Decimals : Decimal numbers can be compared using idea of place value e.g., which is greater ?
(a) 45•32 or 35•69 (b) 1•09 or 1•093
(a) given decimals have distinct whole number part, so we compare whole number part only. whole number part of 45•32 is greater than 35•69, Therefore, 45•32 > 35•69.
(b) whole number part are equal. in decimal part, digit upto hundredth place are equal. But thousandths part of 1•093 is greater than that of 1•09. therefore, 1•093 > 1•09.
• Addition of decimals :
Step 1. Convert given decimals into like decimals.
Step 2. Write addends one under other in column form, keeping decimal points of all addends in same column and digits of same place in same column.
Step 3. Add as in case of whole numbers.
Step 4. In sum, put decimal point directly under decimal points in addends.
• Subtraction of decimals :
Step 1. Convert given decimals into like decimals.
Step 2. Write smaller number under larger one in column form in such a way that decimal points of both numbers are in same column and digits of same place lie in same column.
Step 3. Subtract as we do in case of whole numbers.
Step 4. In difference, put decimal point directly under decimal points of given numbers.
• Using Decimals : Many daily life problems can be solved by converting different units of measurements such as money, length, weight, etc. in decimal form.
Money 100 paise = Rs. 1 1 paise = Rs. 1/100 = Rs. 0•01 5 paise = Rs. 5/100 = Rs. 0•05 105 paise = Rs. 1 + 5 paise = Rs. 1•05 7 rupees 8 paise = Rs. 7 + Rs. 0•08 = Rs. 7•08 7 rupees 80 paise = Rs. 7 + Rs. 0•80 = Rs. 7•80 Length 10 mm = 1 cm 1 mm = 1/10 cm = 0•1 m 100 cm = 1 m 1 cm = 1/100 m = 0•01 m 1000 m = 1 km 1 m = 1/1000 = 0•001 km Weight 1000 g = 1 kg 1 g = 1/1000 kg = 0•001 kg 25 g = 25/1000 kg = 0•025 kg