1. MATHEMATIC IN CONSTRUCTION AND THE BUILT ENVIRONMENT Janine Parry Week 2/3 07/09/15 – 11/09/15

2. Mathematical Techniques and Methods Using a calculator As discussed earlier you will all need a good scientific calculator. Including ADD, SUBTRACT, DIVIDE and MULTIPLY your calculators must have:

3. BIDMAS 46 – 3 x 11 = 46 – 33 = 13 (46 – 3) x 11 = 43 x 11 = 473 Bracketed calculations are done first. Indices or powers are calculated next (e.g. 4 2, where 2 is the power; 4 2 = 4 x 4 = 16). Division and Multiplication take equal priority and are done next. Addition and Subtraction are done last and are of equal priority.

4. Rounding numbers If the next digit is: 5 or more, we 'round up'. 4 or less, it stays as it is. Examples 15645 to the nearest thousand = 16000 15645 to the nearest hundred = 15600.

5. Decimal places Decimal places – again 5 or more, we 'round up'. 4 or less, it stays as it is. For example: 14.6539 = 14.654 (rounded to 3d.p.) 14.65 (rounded to 2 d.p.) 14.7 (rounded to 1 d.p.)

6. Significant figures For example: 14.6539 = 14.654 (rounded to 5 s.f.) 14.65 (rounded to 4 s.f.) 14.7 (rounded to 3 s.f.) 15 (rounded to 2 s.f.)

7. Standard index form (Standard form) Standard form is useful when writing very big or very small numbers which you will often deal with in construction. In standard form a number is always written as: N x 10 n Example write 34 000 000 in standard form. Can be written as: 3.4 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 3.4 x 10 7 Example 0.000821 = 8.21 x 10 -4 Always between 1 and 10 Tell us how many places to move the decimal point

8. Standard index form (Standard form) Adding and subtracting numbers in standard form First you must convert into ordinary numbers, do the calculation, then convert back into standard form. Example 3.2 x 10 4 + 6.78 x 10 5 = 32000 + 678,000 = 710,000 = 7.1 x 10 5 Multiplying and dividing numbers in standard form. To multiply powers you add them e.g. 10 5 x 10 4 = 10 9 To divide powers you subtract them e.g. 10 7 ÷ 10 3 = 10 4

9. Standard index form (Standard form) Zero, negative and fractional powers PowerAnswerExample N0N0 1Anything to the power 0 is equal to 1 N -n N½N½ N 1/3