2.3.2 Standard Form, PT3 Focus Practice


Question 6:
(a)  Round off 0.05079 correct to three significant figures.
(b)  Find the value of 5 × 107 + 7.2 × 105 and state its answer in standard form.

Solution:
(a)  0.05079 = 0.0508 (correct to three significant figures)
(b)  5 × 107 + 7.2 × 105 = 500 × 105 + 7.2 × 105
= (500 + 7.2) × 105
= 507.2 × 105
= 5.072 × 107

Question 7:
(a)  Calculate the value of 70.2 – 3.22 × 8.4 and round off its answer correct to three significant figures.
(b)  Express 840 0.000021  as a number in standard form.

Solution:
(a)  70.2 – 3.22 × 8.4 = 70.2 – 27.048
= 43.152 = 43.2 (correct to three significant figures)

(b)   
840 0.000021 = 8.4 × 10 2 2.1 × 10 − 5 = 8.4 2.1 × 10 2 − ( − 5 ) = 4 × 10 7



Question 8:
Calculate the value of 7 × (2 × 10-2)3– 4.3 × 10-5 and state its answer in standard form.

Solution:
7 × (2 × 10-2)3 – 4.3 × 10-5= 7 × 23 × (10-2)3 – 4.3 × 10-5
= 56 × 10-6 – 4.3 × 10-5
= 5.6 × 10-5 – 4.3 × 10-5
= 1.3 × 10-5

Question 9:
3.17× 10 −8 −1.20× 10 −9 =

Solution:
3.17× 10 −8 −1.20× 10 −9 =3.17× 10 −8 −( 0.120× 10 1 × 10 −9 ) =3.17× 10 −8 −0.120× 10 −8 =( 3.17−0.120 )× 10 −8 =3.05× 10 −8

Question 10:
Express  0.096 ( 2× 10 3 ) 3  in standard form.

Solution:
0.096 ( 2× 10 3 ) 3 = 0.096 8× 10 9 =1.2× 10 −11

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