Fraction and Decimals Blog 7

Fractions and Decimals

Day 7

Hello Learner,

I hope you all have completed the previous work given in earlier blogs. Today, we will be learning more about decimal numbers  and decimal number system.

At the end of today's topic, you will be able to 
(i) compare decimal numbers.
(ii) explain the comparison of decimal number.
(iii) solve problems related to it.

So, let begin the topic.......

                                      DECIMAL NUMBER SYSTEM

In this table, we have written the decimal number in its place-value expansion.

 Let us write the expansion form-

click on the link https://www.youtube.com/watch?v=15zXXjWzh3g

Example 1.  The number 2325 is interpreted in expanded form as −

2325  =   2000    +    300    +  20    +   5
          = 2 X 1000    +  3  X 100  + 2  X 10   + 5 X 1

Example 2: The number 67487 is interpreted in expanded form as-

67487  =   60000  +  7000  +  400  +  80  + 7
            =   6 X 10000  +   7 X 1000  +   4 X 100 +    8 X 10      +    7  X 1

In the same way, decimal number can also be expanded. Let see with example...

Example 3: The number 34.6 is interpreted in expanded form as -

 34.6  =  30  +  4   +   0.1
          
          =  3 X 10   + 4 x 1     +   1
                                               10

Example 4: The number 255.49 is interpreted in expanded form as -

   255.49 =  200  +  50   +  5   +   0.4   + 0.09

   255.49 =  2 X 100   +  5 X 10   + 5 X 1  +   4    +     9
                                                                   10        100

Example 5: The number 287.675 is interpreted in expanded form as -

    287.675 =  200 +  80  + 7  +  0.6  +  0.07  +  0.005

    287.675 =  2 X 100  + 8 X 10  + 7 X 1 +  6   +  7   +      5
                                                                 10     100     1000


I hope you now have clarity in expanded form, let solve the table given below.

                         Comparison of two Decimal Numbers

The decimal point is the most important part of a Decimal Number. Without it we are lost, and don't know what each position means.

17			591
On the left of the decimal point is a whole number (such as 17)
As we move further left, every place gets 10 times bigger.
				The first digit on the right means tenths (1/10).
				As we move further right, every place gets 10 times smaller (one tenth as big).

Let us look at the example, to understand the comparison of two or more decimal numbers.

Rachit brought a toy for Rs 15. 75 whereas Jatin brought the same toy for Rs 15. 55. Who has purchased the toy cheaper?

To solve such problems, where comparison need to be done, we should follow certain steps, that are

Step 1: First compare the digits on the left of the decimal point, starting from the left most. 

In the above case, you can easily see that both the digits 1 and 5, to the left of the decimal point are same. Then, we should follow next step.

Step 2: Compare the digit on the right of the decimal point starting from the tenths place.

In the above case, you can easily see that on the tenth place the digits are 7 and 5. We know that 7 > 5.

Step 3: If the tenth digit is same in two numbers, then compare the digit on the hundredth place and so on.

click the link for detail https://www.youtube.com/watch?v=EX9CdUAMpgE

Let us try to solve question given below... (one is done for you all) 

(i) 35.63 and 35.67 

Here, 35.67 > 35.63 because 35 is common in both numbers and 6 is common in both the numbers in tenths place. At hundredth place, the number given are 3 and 7. we know that 7 > 3, hence 35.67 > 35.63 

(ii) 20.1 and 20.01
(iii)  19.36 and 29.36

Conversion of lower unit of money, length and weight to their higher unit and vice versa.

1 kg                           =  1000 gram
1 Rupee                      = 100 paisa
1km                           = 1000 metre
1 metre                      = 100 cm
1 cm                          = 10 mm
1 litre                         = 1000 ml

click on the link https://www.youtube.com/watch?v=6bQ6HJsAv4A

While converting lower units of money, length and weight, to  their higher unit, decimal are used.
Let understand this, with the help of example...

(i) Rs. 3 = __??___ paisa

we know that Re.1 = 100 paisa, so Rs. 3 will be equal to 3 X 100 = 300 paisa
therefore Rs. 3 = 300 paisa

(ii) 5 kg = ___??___ g
we know that 1 kg = 1000 grams, so 5 kg will be equal to 5 X 1000 = 5000 grams.
therefore 5 kg = 5000 grams

(iii) 7 km = __??____ metre
we know that 1 km = 1000 metre, so 7 km  will be equal to 7 X 1000 = 7000 m
therefore, 7 km = 7000 metre

NOTE: in changing larger unit to smaller unit multiplication is done.

click the link: https://www.youtube.com/watch?v=QF2c3CPhrDk
(iv)  4 paisa =     Rs. __??___

we know that 100 paisa = Re. 1, so 4 paisa will be equal to 4/100 = 0.04= 
Rs. 0.04
therefore,  4 paisa  =  Rs. 0.04 

(v) 6 gram = __??___ kg

we know that 1000 gram = 1 kg, so 6 gram will be equal to 6/1000 = 0.006 kg.
therefore, 6 gram = 0.006 kg

NOTE: in changing smaller unit to larger unit division is done.

(vi) 8 rupees 8 paisa = ____??____ paisa

we know that, Re.1 = 100 paisa, so Rs. 8 will be equal to 800 paisa. 
(we have change higher unit to smaller unit)

8 rupees 8 paisa = 800 paisa + 8 paisa = 808 paisa

I hope, you have clearly understood the topic. Try to solve exercise 2.5 of your text book.

Home Assignment
1. Solve exercise 2.5 in your math notebook. You can take the help of 
2. Do neat and clean work.
3. Comment your doubts in comment box.