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**Standard Form, Ratio, Rates & Proportion**

IGCSE – Chapter 1 Number

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Note 1: Standard Form We use standard form when dealing with very large or very small numbers. a x 10n is in standard form when 1 < a < 10 and n is a positive or negative number.

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Note 1: Standard Form Write the following in standard form. a.) 9000 b.) 350 c.) 0.006 = 9 x 1000 = 9 x 103 Make sure you use this notation and not calculator notation = 3.5 x 100 = 3.5 x 102 = 6 x = 6 x 10- 3 d.) e.) f.) million = 8.37 x 10000 = 8.37 x 104 = 7.5 x = 7.5 x 10- 4 = 1.25 x = 1.25 x 107

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Note 1: Standard Form The speed of light is km/s. Express this speed in cm/s in standard form. x x = = 3 x 1010 Make sure you use this notation and not calculator notation

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Note 1: Standard Form Given that L = 2 , find the value of L in standard form when a = 4.5 x 1012 & k = 5 x 107 Make sure you use appropriate brackets on your calculator = 2 = 600 = 6 x 102 IGCSE Ex 13 pg odd Ex 14 pg odd

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**Note 2: Ratio and Proportion**

The word ‘ratio’ is used to describe a fraction. e.g. If the ratio of your height to your fathers height is 4:5, then you are of your fathers height. e.g. Express the following ratios in the form 1 : n a.) 2:5 b.) 7:8 c.) 33:990 1 : 1 : 30 1 : e.g. Express the following ratios in the form n : 1 a.) 2:5 b.) 3:300 c.) 65:875 : 1 : 1 : 1

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**Note 2: Ratio and Proportion**

Divide $70 between John and Hamish in the ratio of 3:4 Consider that $70 has 7 equal parts(i.e ). Then John receives 3 parts and Hamish receives 4 parts. John receives of $70 = Hamish receives of $70 = $30 $40

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**Note 2: Ratio and Proportion**

A brother and sister share out their collection of 5000 stamps in the ratio 5:3. The brother then shares his stamps with two friends in the ratio 3:1:1, keeping the most for himself. How many stamps do each of his friends receive? Brother receives of 5000 = 3125 stamps His friends each get of the brothers stamps = 625 stamps IGCSE Ex 15 pg odd

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**Note 2: Ratio and Proportion**

Proportion – Finding a unit quantity If a wire of length 5 metres costs $35, find the cost of a wire of length 75 cm 500 cm costs 3500 cents 1 cm costs = 7 cents 75 cm costs 7 x 75 = 525 cents = $5.25

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**Note 2: Ratio and Proportion**

If it takes 6 men 4 days to dig a hole 3 feet deep, how long will it take 10 men to dig a hole 7 feet deep? 6 men 4 days (3 ft) of 3 ft is 7 ft 1 man 24 days (3 ft) 10 men days (3 ft) 10 men x = days = 5.6 days IGCSE Ex 16 pg odd

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**Note 3: Approximations & Estimation**

Write the following correct to the nearest: Whole Number 3 sf 2 dp 3.121 0.589 3.255 9.896 0.0820 3 3.12 3.12 1 0.589 0.59 3 3.26 3.26 9.90 10 9.90 0.0820 0.08

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**Note 3: Measurements & Bounds (Limits of accuracy)**

Remember that measurements are approximate. e.g. The length of a fabric is measured to 145 cm to the nearest cm. The actual length is between cm and ….. 144.5 < length < 145.5 Lower bound (limit) Upper bound (limit)

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**Note 3: Measurements & Bounds (Limits of accuracy)**

Remember that measurements are approximate. e.g. The weight of a butterfly is given as g. The actual weight is between and g g < weight < 0.0315 0.0325 Upper bound (limit) Lower bound (limit) IGCSE Ex pg 9 Ex 10 pg odd Ex 11 pg odd

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**Note 4: Currency Exchange**

An application of how we use proportion. e.g. The following are exchange rates for NZD ($). Country Exchange Rate U.K. (pounds) £0.58= $1 Canada ($) $1.276 CAD = $1 Euro (euros) €0.785 = $1 Argentina (pesos) 0.897ARPO = $1 Convert $ to euros Convert £500 to NZD $ $1 = €0.785 £0.58= $1 $28 = €0.785 x 28 £1= $28 = €21.98 £500=$862.07

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**Note 5: Speed, distance & time**

Great care must be taken with units in these problems. e.g. How long is a train which passes a signal in twenty seconds at a speed of 108 km/hr?. T = 20 s x T = hr D = S x T D = 108 km/hr x hr D = 0.6 km D = 600 m

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**Note 5: Speed, distance & time**

Great care must be taken with units in these problems. e.g. An earthworm of length 15cm is crawling along at 2 cm/s. An ant overtakes the worm in 5 seconds. How fast is the ant walking?. How far does the earthworm travel in 5 seconds? x 5 s = 10 cm The ant must overtake the length and distance travelled 10 cm + 15 cm = 25 cm (in 5 seconds) IGCSE Ex pg 18-19 Ex pg 29-30 The ant’s speed is = 5

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