MATHEMATIC IN CONSTRUCTION AND THE BUILT ENVIRONMENT

Janine Parry

Week 2/3

07/09/15 – 11/09/15

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:

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. 42, where 2 is the power; 42 = 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.

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.

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.)

Significant figuresFor 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.)

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 10n

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 107

Example

0.000821 = 8.21 x 10-4

Always between 1 and 10Tell us how many places to move the decimal point

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 104 + 6.78 x 105

= 32000 + 678,000

= 710,000

= 7.1 x 105

Multiplying and dividing numbers in standard form.

To multiply powers you add them e.g. 105 x 104 = 109

To divide powers you subtract them e.g. 107 ÷ 103 = 104

Standard index form (Standard form)Zero, negative and fractional powers

Power Answer Example

N0 1 Anything to the power 0 is equal to 1

N-n 3-4 = =

N½ 9½ = 3

N1/3 641/3 = = 4