Question
Let x = 1352.406 and y = 0.0001352406
(a) State the value of x correct (i) to 2dp. (ii) to 3sf. (iii) to 2sf.
(b) State the value of y correct (i) to 5dp. (ii) to 3sf. (iii) to 2sf.
(c) State the value of x in the form \(a\times 10^k\) where 1≤a<10 and k∈\(\mathbb{Z}\)
(d) State the value of y in the form \(a\times 10^k\) where 1≤a<10 and k∈\(\mathbb{Z}\).
Answer/Explanation
Ans:
(a) (i) 1352.41 (ii) 1350 (iii) 1400
(b) (i) 0.00014 (ii) 0.000135 (iii) 0.00014
(c) 1.35×103
(d) 1.35×10-4
Question
The value of x correct to 3 sf is 34 500. The value of y correct to 3 sf is 0.0301.
The value of z correct to 2 dp is 15.30. The value of w correct to 3 sf is 145.
Find the range of the possible values of x, y, z, w.
Answer/Explanation
Ans:
(a) 34450 ≤ x < 34550
(b) 0.03005 ≤ y < 0.03015
(c) 15.295 ≤ z < 15.305
(d) 144.5 ≤ w < 145.5
Question
By using a LHS to RHS proof or vice versa, prove the following identities
(a) (a +2b)(2a +b) ≡ 2(a2+b2)+ 5ab
(b) \(a^2-b^2≡(a-b)(a+b)
(c) \(a^3-b^3≡(a-b)(a^2+ab+b^2)\)
(d) \(a^3+b^3≡(a+b)(a^2+ab+b^2)\)
Answer/Explanation
Ans:
(a) LHS to RHS proof
(b)(c)(d) RHS to LHS proof