I. Decimal Fractions : Fractions during which denominators are powers of 10 are generally known as decimal fractions.

hundredth =.01;

hundreths=.99;7/1000=7 thousandths=.007,and many others

with it as many zeros as is the variety of digits after the decimal level. Now,

take away the decimal level and scale back the fraction to its lowest phrases.

0.25=25/100=1/4;2.008=2008/1000=251/125.

III. 1. Annexing

zeros to the acute proper of a decimal fraction doesn’t change its worth

and many others.

comprise the identical variety of decimal locations, then we take away the decimal

signal.

1.84/2.99 = 184/299 = 8/13;

0.365/0.584 = 365/584=5

1. Addition and Subtraction of Decimal

Fractions : The

given numbers are so positioned underneath one another that the decimal factors lie in a single column. The numbers so organized can now be added or subtracted within the common approach.

2. Multiplication of a Decimal

Fraction By a Energy of 10 : Shift the decimal level to the proper by as many locations as is the ability of 10.

= 730.

3. **Multiplication
of Decimal Fractions **: Multiply the given numbers contemplating them with out the decimal level. Now, within the product, the decimal level is

marked off to acquire as many locations of decimal as is the sum of the variety of decimal locations within the given numbers.

product (.2 x .02 x .002). Now, 2x2x2 = 8. Sum of decimal locations = (1 + 2 + 3)

= 6. .2 x .02 x .002 = .000008.

4. Dividing a

Decimal Fraction By a Counting Quantity : Divide the given quantity with out contemplating the decimal level, by the given counting quantity. Now, within the quotient, put the decimal level to provide as many locations of decimal

as there are within the dividend.

quotient (0.0204 + 17). Now, 204 ^ 17 = 12. Dividend comprises 4 locations of

decimal. So, 0.0204

*+*17 = 0.0012.

Fraction : Multiply each the dividend and the divisor by an appropriate energy

of 10 to make divisor an entire quantity. Now, proceed as above.

Thus,

0.00066/0.11 =

(0.00066*100)/(0.11*100) = (0.066/11) = 0.006V

descending order of magnitude. Then, convert every one of many given fractions in

the decimal kind, and organize them accordingly.

fractions 3/5, 6/7 and seven/9 in descending order.

0.777….

VI. Recurring Decimal : If in a decimal fraction, a determine or a set of figures is

repeated repeatedly, then such a quantity is known as a *recurring decimal. *In a recurring decimal, if a single determine is repeated,

then it’s expressed by placing a dot on it. If a set of figures is repeated,

it’s expressed by placing a bar on the set

22 /7 = 3.142857142857…..= 3.142857

decimal level are repeated, is known as a pure recurring decimal.

Decimal Into Vulgar Fraction : Write the

repeated figures solely as soon as within the numerator and take as many nines within the

denominator as is the variety of repeating figures.

,0.5 = 5/9; 0.53 = 53/59 ;0.067 =

67/999;and many others…

Combined Recurring Decimal: A decimal fraction during which some figures don’t repeat and

a few of them are repeated, is known as a combined recurring decimal. e.g., 0.17333 =

0.173.

shaped by all of the digits after decimal level (taking repeated digits solely as soon as)

and that shaped by the digits which aren’t repeated, Within the denominator, take

the quantity shaped by as many nines as there are repeating digits adopted by as

many zeros as is the variety of non-repeating digits.

1/6;

Formulae :

*b)(a- b) =*(a

^{2}– b

^{2}).

b)

^{2}= (a

^{2}+

*b*2ab).

^{2}+(a – b)

^{2}= (a

^{2}+

*b*

–2ab).

^{2}–

^{2}= a

^{2}+

*b*(ab+bc+ca)

^{2}+ c^{2}+2^{3}

+ b

^{3}) = (a + b) (a

^{2}– ab

*+*b

^{2})

^{3}

– b

^{3}) = (a – b

*)*(a

^{2}

*+*ab

*+*b

^{2}).

^{3}

+ b

^{3}+ c

^{3}– 3abc) = (a + b + c)

*(a*

^{2}+ b

^{2}

+ c

^{2}-ab-bc-ca)

When a + b + c = 0, then a

^{3}

+ b

^{3}+ c

^{3}

*=*3abc