###### Multiplication of decimals

we can multiply the decimals by adding them ex. 3×0.7 is 0.7+0.7+0.7=2.1

see the models in page no. 116.

###### multiplying with out model

ex. 1.25×7

multiply as a whole number and ignore the decimals. Count the total numbers of the decimals places in both numbers.from right cont the same number of decimal places and put the point there.ie. 125×7=875 after put the point we will get 8.75.

###### zeros in the products

ex. 0.02×3 as whole number we will get 6. but the total decimal place is 2 so we can add one more zero in the left side of 6 and can make 2 decimal place. 0.06.

ex2. 0.05×6 as a whole number we will get 30. after punting the decimal place we will get 0.30. but remember the the zeros of the end of the decimal number have no values. so it will become 0.3.

see common mistakes in p-117.

###### Multiplication by 10, 100, 1000

multiplying by 10 move the decimal point **one** place to right.

multiplying by 100 move the decimal point **two** place to right.

multiplying by 1000 move the decimal point **three** place to right.

ex 10×5.623=56.23

ex2 100×5.623=562.3

ex3 1000×5.623=5623

**see p-118 for exercise 8A**

###### Dividing decimal with whole numbers

ex1. 0.8/4 which means divide 0.8 in equal 4 parts. models can be see in p-119.0.8/4=0.2

ex.2 p-119. 1.33/7 we can divide as whole number and put the same decimal place in the dividend to the quotient. So 1.33/7=0.19 we can check the answer by dividend= quotient x divisor.

###### divisor smaller than dividend

ex 4.35/3 this one can also divide as whole number. and put the decimal place as same number in the dividend. So 4.35/3=1.45.

###### reminders while dividing decimals

If we get reminder while dividing the decimals, then put the decimal point in the quotient as same as the dividend. Once the quotient have the decimal point we can add zeros in the dividend and can complete the division.

ex. 3.5/2 = 1.75

**see p-120 for exercise 8b**

###### division by 10.100,1000

To divide the decimal number with 10, 100, 1000 we can move the decimal point to left as much zeros in in the divisor.

ex. 321.5/10=32.15, 321.5/100=3.215, 321.5/1000=0.3215.

**see p-121 for exercise 8c.**

###### decimals and money

1 Rs is 100 paise. the model can be see in p-122. 50 paise can be write 50/100 rupee. that s 0.50 rupee.

So 1rupee+50 paise can be written as 1+50/100=1×50/100=1.50 rupee.

75 paise = 75/100= 0.75 rupee.

###### multiplication and division with money

**Unitary method: I**n this method we can find the unit price of an item.

ex. A shop have he price for 8 lemon is Rs 20. how can we find the price for 1 lemon. price for 1 lemon is 20/8. we can divide the rupees as same as whole number. but keep 2 decimal places in the quotient. Ie. 20/8 we will get 2.5. but we make it 2.50, to keep 2 decimal places in the rupee division. if the other shop have Rs 13.50 for 6 lemon, how we can compere the price for both shop. For that we have to find the price for the 1 lemon in each shop by dividing. After that we can compare the price for each shop. 13.50/6=2.25 a(We can divide by keeping decimal point also). The second shop have the low price. See more ex. in p-123. multiplication can do as same as whole number. See p-124 for exercise 8D. The above method is find the price of the unit, or unit price so it is called **unitary method.**

See chapter checkup in p-125,126.