Decimals are the fraction with denominator 10, 100, 1000 etc. Or we can also say that decimals are the number with decimal points. In decimal number they are not write with denominator but with decimal point. ex. 2.3, 5.67 and it is read out two point 3 and five point six seven. So the decimal number have a whole part and fraction part. please see the fig. for more details.
Consider an graph paper with 10 CM square. And if we cut the square in equal 10 parts, then we can say that each part is 1/10 of the whole. And if we again divide the 1/10 parts in 10 equal parts then each part will become 1/100 of the whole. And we can again divide the 1/100 part in equal 10 parts then it will become the 1/1000 of the whole. This one we can practice in graph paper by shading. This 1/10, 1/100, 1/1000 is called decimal fractions.
We can also write the same thing in 0.1, 0.01, 0.001, because we know that to divide a number with 10, 100, 100. we have to just shift the decimal point from write to left. Or we can also do the normal division.
If there is no whole number part in a decimal number, then we can put one zero on the left side of the decimal point. This type of decimal number is called proper decimals. ex 0.763
If the decimal number have both whole number part and fractional part then it can called improper decimals. ex 4.345
If write zeros to the extreme left (in integer number part) , the value of the number will not change. ex. 00678.4 . And if add zeros on the extrm right ( fractional Part) the value will not change.ex. 45.650000 .
the place value of the first number after the decimal point from left Is 1/10. And this is called Tenths. So the value of the tenths place number 1,4,7 are 1/10, 4/10, 7/10 as the place value is 1/10. It can also write as 0.1, 0.4, 0.7.
the place value of the Second number after the decimal point from left Is 1/100. And this is called Hundredths. So the value of the hundredths place number 1,4,7 are 1/100, 4/100, 7/100 as the place value is 1/100. It can also write as 0.01, 0.04, 0.07.
the place value of the Third number after the decimal point from left Is 1/1000. And this is called Thousandths. So the value of the thousandths place number 1,4,7 are 1/1000, 4/1000,7 /1000 as the place value is 1/1000. It can also write as 0.001, 0.004, 0.007.
Representing decimals on a number line
How we can represent 0.6 on the number line. We know that 0.6 is greater than 0 and less than one. So we have to draw a number line with one unit length. And we also know that 0.6 is on the tenths place. So we need to divide our number line in equal 10 part, and we can mark the sixth division as 0.6. Please see the bellow fig.
in fig-2 we can see the 1.2 is marked on the number line. Here the 1.2 is grater than 1 and less than 2. So we have to draw a number line with 2 units of length. And the .2 is in the tenths place so we have to divide the each unit in equal 10 parts. As the 1.2 Have one once, we have to take one complete unit in the number line first. Then we have to take 2 one by ten unit. And can mark 1.2 as shown in the fig. Now we can try with some more number in number line.
Fraction as decimals
We all ready know how fraction with denominator 10,100,1000 can write as decimals. Now we can study how we can make all fractions in decimals.
Ex. 11/5, solution, First we can convert this fraction with 10 denominator by multiplying both numerator and denominator by 2. So now it will become 22/10 and which =2.2 in decimal form. Now yo can try with any fractional number. We can also convert the fraction to decimal by normal division. When we divide 11/5 then we will get 2.2 as quotient.
Decimals are fractions
Now we can study how can convert a decimal to fraction .
Ex. 1.2 solution: 1.2=1+2/10, which = 10/10+2/10 = 12/10.
Now we can try with other numbers…
In order to compare two decimals we have to compare the whole part first. If the whole part of one decimal is big then that number will be the bigger one. If whole part is same then we have to compare the tenth place. If the tenth place is bigger for one number then it will be the bigger number. If the tenth place is also same then we have to check the hundredth place and the thousandth place so on.
compare 32.55 and 32.5
32.55 = 32+5/10+5/100, 32.5=32+5/10+0/100, Here the whole part and tenth part are same for both number but the 100th part is bigger for the first number. So the number 32.55 is the bigger one. Now we can try with more numbers.
In length we can say
1m =100cm Or 1cm = 1/100m =0.01m
1cm=10mm 0r 1mm=1/10cm=0.1cm
In order to convert m to cm we have to multiply with 100. And from centimeter to meter we have to divide with 100. (from big unit to small unit multiplication and from small unit to big unit division).
By this we can convert a given length in mm,cm,m or combination of any two.
ex. 156 cm = 1.56m 246cm= 2m and 46 cm or 2.46m.
We can also try with many other length.
1000g=1kg or 1gram = 1/1000kg
2350g can be write as 2000g + 350g That means 2kg 350g.
To convert from kg to gram we have to multiply with 1000. I f we need convert fro gram to kg we have to divide with 1000. (from big unit to small unit multiplication and from small unit to big unit division).
Now we can try with different weight.
Measurement of capacity
1000ml=1l or ml=1/1000l
In order to convert litter to ml we have to multiply with 1000. And to convert ml to l we have to divide. (from big unit to small unit multiplication and from small unit to big unit division).
Rupees and paise
100 paise = 1 rupee or 1paise = 1/100 rupee..
to convert rupee to paise we have to multiply with 100. In order to convert paise to rupee wee need to divide with 100. (from big unit to small unit multiplication and from small unit to big unit division). Try with exercise
Adding of decimal numbers
We can only add like decimals. If the decimals are like decimals then we can add them abnormal as natural number or integer numbers. If the number of decimal places of two or more number are same then they are called like decimals.Ex. 4.02, 5.67 both number have two decimal places so they are like decimals. If two numbers are not like decimal, we can make them like by adding zeros in the write side of the decimal places. Ex. 2.3, 4 .78, are not like but 2.30,4.78 are like. Now we can practice more number for decimal addition.
Subtraction of decimals numbers
Subtraction can also do with like decimals. If both decimals are like decimals, then we can do the subtraction as normal as in intriguer and natural numbers.