By J O Bird

An creation to center arithmetic required for engineering learn contains multiple-choice questions and solutions, labored difficulties, formulae, and exercises.

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2890625 (6) 12. Convert (a) 5F16 into its decimal equivalent (b) 13210 into its hexadecimal equivalent (c) 1101010112 into its hexadecimal equivalent (6) 14. 076 (c) 145 Convert the following binary numbers to decimal form: 13. 0419 2 3 × 2 × 22 (23 × 16)2 (b) 4 2 (8 × 2)3 1 42 (4) 11. 64 g (2) (a) 9. 1875 Evaluate (b) correct to 1 decimal place 4. 98 (7) 15. 6 km = 1 mile, determine the speed of 45 miles/hour in kilometres per hour (3) 16. 1 Basic operations Algebra is that part of mathematics in which the relations and properties of numbers are investigated by means of general symbols.

1 Basic operations Algebra is that part of mathematics in which the relations and properties of numbers are investigated by means of general symbols. For example, the area of a rectangle is found by multiplying the length by the breadth; this is expressed algebraically as A = l × b, where A represents the area, l the length and b the breadth. The basic laws introduced in arithmetic are generalised in algebra. Let a, b, c and d represent any four numbers. Then: (i) a + (b + c) = (a + b) +c Replacing p, q and r with their numerical values gives: 3 3 2 1 3 3 3 = 4 × 2 × 2 × × × × = 27 2 2 2 2 4 p 2 qr 3 = 4(2)2 1 2 Problem 3.

500 3 2 5 1. 1 3. (a) 101010 (b) 111000 (c) 1000001 (d) 10111000 [(a) 4210 (b) 5610 (c) 6510 (d) 18410] 4. 3437510 0 1 (least significant bit) For fractions, the most signiﬁcant bit of the result is the top bit obtained from the integer part of multiplication by 2. The least signiﬁcant bit of the result is the bottom bit obtained from the integer part of multiplication by 2. 1012 Problem 4. 01012 0 1 1 0 1 1 1 1 Thus 4710 = 1011112 Now try the following exercise Exercise 11 Problem 5. 40625 3 2 5 0.