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Standard Form, Ratio, Rates & Proportion

Standard Form, Ratio, Rates & Proportion. IGCSE – Chapter 1 Number. Note 1 : Standard Form. We use standard form when dealing with very large or very small numbers. a x 10 n is in standard form when 1 < a < 10 and n is a positive or negative number. Note 1 : Standard Form.

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Standard Form, Ratio, Rates & Proportion

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  1. Standard Form, Ratio, Rates & Proportion IGCSE – Chapter 1 Number

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

  3. Note 1: Standard Form Write the following in standard form. a.) 9000 b.) 350 c.) 0.006 = 9 x 103 = 9 x 1000 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.) 83700 e.) 0.00075 f.) 12.5 million = 8.37 x 10000 = 8.37 x 104 = 7.5 x = 7.5 x 10-4 = 1.25 x 107 = 1.25 x 10000000

  4. Note 1: Standard Form The speed of light is 300 000 km/s. Express this speed in cm/s in standard form. x x = 30000000000 = 3 x 1010 Make sure you use this notation and not calculator notation

  5. 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 13-14 odd Ex 14 pg 14-15 odd

  6. 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. Express the following ratios in the form 1 : n e.g. a.) 2:5 b.) 7:8 c.) 33:990 1 : 30 1 : 1 : Express the following ratios in the form n : 1 e.g. a.) 2:5 b.) 3:300 c.) 65:875 : 1 : 1 : 1

  7. 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. 3 + 4). Then John receives 3 parts and Hamish receives 4 parts. $30 John receives of $70 = Hamish receives of $70 = $40

  8. 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 15-16 odd

  9. 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

  10. 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 = 5 days = 5.6 days IGCSE Ex 16 pg 17-18 odd

  11. Note 3: Approximations & Estimation Write the following correct to the nearest: 3 3.12 3.12 0.589 1 0.59 3.26 3 3.26 9.90 9.90 10 0.0820 0 0.08

  12. 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 144.5 cm and 145.4999999….. 144.5 < length < 145.5 Lower bound (limit) Upper bound (limit)

  13. Note 3: Measurements & Bounds (Limits of accuracy) Remember that measurements are approximate. e.g. The weight of a butterfly is given as 0.032 g. The actual weight is between and 0.0315 g 0.0325 g < weight < 0.0315 0.0325 Upper bound (limit) Lower bound (limit) IGCSE Ex 9 pg 9 Ex 10 pg 10-11 odd Ex 11 pg 11-12 odd

  14. Note 4: Currency Exchange An application of how we use proportion. e.g. The following are exchange rates for NZD ($). Convert $ 28.00 to euros Convert £500 to NZD $ $1 = €0.785 £0.58= $1 $28 = €0.785 x 28 £1= $28 = €21.98 £500=$862.07

  15. Note 5: Speed, distance & time D S T 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 = 0.005556 hr D = S x T D = 108 km/hr x 0.005556 hr D = 0.6 km D = 600 m

  16. Note 5: Speed, distance & time D S T 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? 2 x 5 s = 10 cm The ant must overtake the length and distance travelled 10 cm + 15 cm = 25 cm (in 5 seconds) IGCSE Ex17 pg 18-19 Ex25 pg29-30 The ant’s speed is = 5

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