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Practice each question, then open the answer or worked solution.
In standard form, the number 72105.4 is written as 7.21054 × 10n where n is equal to
(a) 2 (b) 3 (c) 4 (d) 5
Solution:-
(c) 4
Any number can be expressed as a decimal number between 1.0 and 10.0 (including 1.0) multiplied by a power of 10. Such form of a number is called its standard form or scientific notation.
72105.4 is written as 7.21054 × 104
Square of (-2/3) is
(a) -2/3 (b) 2/3 (c) -4/9 (d) 4/9
Solution:-
(d) 4/9
Square of (-2/3) is = -22/32
= (-2 × -2)/(3 × 3)
= 4/9
cube of (-1/4) is
(a) -1/12 (b) 1/16 (c) -1/64 (d) 1/64
Solution:-
(c) -1/64
Cube of (-1/4) is = -13/43
= (-1 × -1 × -1)/(4 × 4 × 4)
= -1/64
Which of the following is not equal to (-5/4)4?
(a) (-5)4/44 (b) 54/(-4)4
(c) –(54/44) (d) (-5/4) × (-5/4) × (-5/4) × (-5/4)
Solution:-
(c) –(54/44)
Which of the following is not equal to 1 ?
(a) (23 × 33)/(4 × 18) (b) [(-2)3 × (-2)4] ÷ (-2)2
(c) (30 × 53)/(5 × 25) (d) 24/(70 + 30)3
Solution:-
(d) 24/(70 + 30)3
= 24/(1 + 1)3
= 24/23
(2/3)3 × (5/7)3 is equal to
(a) ((2/3) × (5/7))9 (b) ((2/3) × (5/7))6
(c) ((2/3) × (5/7))3 (d) ((2/3) × (5/7))0
Solution:-
(c) ((2/3) × (5/7))3
For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n.
am × bm = (ab)m
In standard form, the number 829030000 is written as K × 108 where K is equal to (a) 82903 (b) 829.03 (c) 82.903 (d) 8.2903
Solution:-
(d) 8.2903
Any number can be expressed as a decimal number between 1.0 and 10.0 (including 1.0) multiplied by a power of 10. Such form of a number is called its standard form or scientific notation.
829030000 is written as 8.2903 × 108
Which of the following has the largest value?
(a) 0.0001 (b) 1/10000 (c) 1/106 (d) (1/106) ÷ 0.1
Solution:-
(a) 0.0001 and (b) 1/10000 = 0.0001
In standard form 72 crore is written as
(a) 72 × 107 (b) 72 × 108 (c) 7.2 × 108 (d) 7.2 × 107
Solution:-
(c) 7.2 × 108
Any number can be expressed as a decimal number between 1.0 and 10.0 (including 1.0) multiplied by a power of 10. Such form of a number is called its standard form or scientific notation.
72 crore is written as = 72,00,00,000 = 7.2 × 108
For non-zero numbers a and b, (a/b)m ÷ (a/b)n, where m>n, is equal to
(a) (a/b)mn (b) (a/b)m + n (c) (a/b)m – n (d) ((a/b)m)n
Solution:-
(c) (a/b)m – n
For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n,
am ÷ an = am–n , m>n