Page 55 - SM inner class 7.cdr

3. Eval u ate the fol low ing ex pres sions.
3 2
é æ - ö 3 0 ù é æ - ö 3 2 ù
7 0
2 2
3 2
2
(a) ( )1 2 3 ´ ( ) (b) [(-3 ) ] ´ [(-3 ) ] (c) ê ç ÷ ú ´ ç ê ÷ ú
ê è 4 ø ú ê ë è 4 ø ú
ë
û
û
- 3 - 6 5 -5
1 æ ö 1 æ ö æ - ö 2 æ - ö 2
ç ÷ ´ ç ÷ ç ÷ ´ ç ÷
æ 2 3 ö 2 è ø 2 è ø è 9 ø è 9 ø
(d) ç ÷ (e) (f)
6
3
è 2 ¸ 2 ø 1 æ ö - 5 æ ö 3 4 æ ö 3 -4
ç ÷ ç ÷ ´ ç ÷
2 è ø è ø 2 è ø 2
- 3 - 5 - 5 - 4
1 æ ö 1 æ ö 2 æ ö 2 æ ö
ç ÷ ç ÷ ç ÷ ´ ç ÷ 3 0 - 3 -2 -3 -4
1
1
2 æ ö
2 æ ö
æ
2 æ ö
æ ö
æ ö
(g) 3 è ø - 3 è ø (h) 3 è ø 3 è ø (i) ç ÷ ´ ç ÷ ´ ç ÷ (j) ç - ö 1 ÷ + ç ÷ + ç ÷
1 æ ö - 4 1 æ ö - 6 2 æ ö - 4 2 æ ö - 4 3 è ø 3 è ø 3 è ø è 2 ø è ø 3 è ø 4
ç ÷ ç ÷ ç ÷ ¸ ç ÷
3 è ø 3 è ø 3 è ø 3 è ø
4. Ex press the fol low ing in stan dard form :
(a) 6000 (b) 0.0000002877 (c) 18000000 (d) 27thousandths.
5. Ex press each of the fol low ing in usual form.
(a) 662 10. ´ - 9 (b)14 10. ´ 13 (c) 4 10´ - 8 (d)126 10. ´ 8
Summary
m The exponent of a number tells us how many times a number (base) is multiplied with itself.
m While multiplying two rational numbers with the same base, we add their exponents but the base remains
n
+
unchanged. i e a. . m ´ a = a m n
m While multiplying two national numbers having same exponent, the product of two bases is written with the
n
n
given exponent. i.e. a ´ b = ( ab) n
m The division of two rational numbers with the same base can be performed by subtracting their exponents. i.e.
n
a m ¸ a = a m - n
m To raise a power to another power, we just write the product of two exponents with the same base.
m n
.
.
i e a ) = a mn
(
m Any non-zero rational number with zero exponent equals to 1, i e a. . 0 = 1
m Any non-zero rational number with a negative exponent equals to its reciprocal with the same but positive
1
m
-
exponent. i e. . a =
a m
n
n
m (– )a is positive, if n is an even integer and (-a is negative, if n is an odd integer.
)
n
m We can express very large and small numbers in special form such as K ´ 10 , where n is any integer. This
form of writing numbers is known as scientific notation. This form of numbers is also called the standard from.
Review Exercise
1. Write the ex panded form of the fol low ing :

(a) p 7 (b) l 4 (c) s 9 (d) d 6 (e) z 5
2. Write the fol low ing in ex po nen tial form :
(a) a a a´ ´ ´ ……………… ' 'l times. (b) 5 5 5 5´ ´ ´ ……………… ' 'n times
(c) q q q q q´ ´ ´ ´ ............ 15 times.

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Mathematics In Focus - 7