**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 1.

**Write addends one under other in column form, keeping decimal points of all addends in**

Step 2.

Step 2.

**same column and digits of same place in same column.**

**Add as in case of whole numbers.**

Step 3.

Step 3.

**In sum, put decimal point directly under decimal points in addends.**

Step 4.

Step 4.

**•**

**Subtraction of decimals :**

Step 1.Convert given decimals into like decimals.

Step 1.

**Write smaller number under larger one in column form in such a way that decimal points of**

Step 2.

Step 2.

**both numbers are in same column and digits of same place lie in same column.**

**Subtract as we do in case of whole numbers.**

Step 3.

Step 3.

**In difference, put decimal point directly under decimal points of given numbers.**

Step 4.

Step 4.

**•**

**Using Decimals :**Many daily life problems can be solved by converting different units of measurements such as

**money, length, weight, etc. in decimal form.**

**100 paise = Rs. 1**

Money

Money

**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**