Page 71 - Maths On the GO Class 7

4. Simplify the following and express as a rational number :

2
3
1
3
3
æ ö 3 æ ö 4 æ ö 2 æ ö 4 æ -1 ö 5 3 æ ö 2
(a) ç ÷ ´ ç ÷ (b) ç ÷ ¸ ç ÷ (c) ç ÷ ´2 ´ ç ÷
4
è 9 ø è 4 ø è 8 ø è 4 ø è 2 ø è ø
2
3
7
ü
2
æ
æ ö
0
0
´
(d) (15 ´ 40 0 ) (3 - 2 0 ) (e) ç ÷ ´ ç - 3 ö 3 æ ö 2 (f) ì æ -3 ö 3 æ -5 ö ÷ ý ´ 4 2
÷ ´ ç ÷
÷ - ç
ç í
è 3 ø è 5 ø è 2 ø î è 4 ø è 2 ø þ
5. Which is greater in each of the following pairs?
3
2
3
5
7
2
(a) (2 2 3 2 2 (b) 4 ´ 4 or 3 ´ 2 5 (c) 3 ¸ 3 or 3 ´ 3 3
) or (4
)
3 0 12 0 3 4 2 2 3 3 6 4
)
(d) 18 ´ 18 or 2 ´ 2 (e) 2 ´ 2 or 3 ´ 4 (f) 7 ¸ 7 or (-7 ) ¸ (-6
2
a æ ö 2 æ ö -1 æ ö 3
2
a
6. If = ç ÷ ¸ ç ÷ , find ç ÷ .
3
3
b è ø è ø è b ø
7. If 2 n- 7 ´ 5 n- 4 =1250, find the value of n.
æ -1 ö 1
8. By what num ber should ç ÷ be di vided so that the quo tient is equal to ?
è 30 ø 6
2
2
)
)
9. By what num ber should (-5 be mul ti plied so that the prod uct is equal to (25 ?
Scientific Notation or Standard Form of Large (a) 6,759,800,000 (b) 7,530,000,000
Numbers (c) 381.975 (d) 340 000 000 000, , ,
Any number that can be expressed as a product of a So lu tion :
number between 1 and 10 and a power of 10 is said
(a) 6,759,800,000 = 6.7598 × 1,000,000,000
to be in its standard form.
.
=6 7598 10 9
´
In general, a number in the form of a ´10 n (where
(b) 7,530,000,000 = 7.53 ´ 1,000,000,000
a
1 £ < 10 and n is an integer) is said to be in standard
= 7.53 ´ 10 9
form.
(c) 381.975 = 3.81975 ´ 100
For example :
= 3.81975 ´ 10 2
Mass of the Uranus
(d) 340,000,000,000 =3 4. ´ 100,000,000,000
,
,
,
,
,
,
,
=86 800 000 000 000 000 000 000 000 kg
,
.
´
=8 68 10 000 000 000 000 000 000 000 000 kg =3 4 10 11
,
.
,
,
,
,
,
,
,
´
25
´
=8 68 10 kg Example : Write each of the fol low ing in usual form :
.
(a) 4 3 10. ´ 3 (b) 5838 10. ´ 6
Mass of the Earth
=5972 000 000 000 000 000 000 000 kg So lu tion :
,
,
,
,
,
,
,
,
3
.
.
,
´
´
,
,
,
,
,
.
=5972 1000 000 000 000 000 000 000 000 kg (a) 4 3 10 = 4 3 1000
,
,
,
´
24
.
=5972 10 kg = 4300
´
6
,
,
.
(b) 5838 10 =5838 1000 000
.
´
´
Solved Examples
,
,
=5838 000
Example : Ex press the fol low ing num bers in stan dard
form :
Exponents 71