CONNECT: Currency, Conversions, Rates

Transcription

1 CONNECT: Currency, Conversions, Rates CHANGING FROM ONE TO THE OTHER Money! Finances! $ We want to be able to calculate how much we are going to get for our Australian dollars (AUD) when we go overseas, and how much we are going to get for the foreign currency (whatever it may be) when we return. Hence, the need for Conversions. Let s say we are going to New Zealand. We have $100 (AUD) to spend. How much is that in New Zealand currency (NZD)? There are many conversion sites on the internet but we are determined to calculate this by ourselves! What we do need from the internet, though, is the conversion rate. (Sometimes we will know a conversion rate, for example later we will talk about measurement where we will know some of the appropriate conversion rates). With money, however, we can t know the rate because the rates change all the time depending on the financial markets. At the time of writing, 1 AUD is worth NZD. Right, we know what we need to know! Now, we just have to work it out. If 1 AUD is worth NZD, then 2 AUD will be worth 2 x NZD and 3 AUD will be worth 3 x NZD and so on. In fact, to convert any amount of AUD to NZD, we multiply the number of AUD by the conversion rate ( ) to find the equivalent NZD. 100 AUD is therefore (today) worth 100 x NZD, and so we would receive New Zealand Dollars for our $100 Australian. Change $ (AUD) to New Zealand dollars. We would multiply by You would certainly use your calculator here, and you would round to the nearest 10c because New Zealand does not have 1c, 2c, or 5c coins. Source: 11/1/12. 1

2 x = This would be rounded to , so we would get $ NZD for our $ AUD. This looks nicer and probably easier to follow using a table like this: AUD Calculation NZD x ( 2.60) 3 3 x ( 3.90) x ( ) x ( ) ( means is roughly equal to) As long as we know what 1 unit is worth, we can change any amount. But what if we want to come back to Australia from New Zealand? We would like to change our NZD back to our familiar AUD. We brought back NZD. How much should we get in AUD? This time we do NOT know the conversion rate because we only know it going from AUD to NZD, not vice versa. So, we know AUD NZD We need to know AUD????? 1 NZD 2

3 If you look at the two tables, you can see that to get from to 1 in the NZD column, we would divide by To retain the equivalence for the AUD, we do the same that is we divide 1 AUD by to get what goes in the????? slot: AUD Calculation NZD (= ) = , which becomes our new conversion rate. So, $53.70 NZD is worth x AUD, which means we would get $41.43 AUD for our $53.70 NZD. This will be clearer in a new table, with the NZD first this time, and with the new conversion rate. NZD Calculation AUD x ( 41.43) If you know a conversion rate, then you can multiply the quantity you need to change by the conversion rate to get to the new currency. If you want to come backwards from the currency, divide 1 by the conversion rate, then multiply that new figure by the amount you want to change. The above method is certainly not the only method for conversions. You may prefer another method. More examples. Today, 1 AUD is worth USD. How many US Dollars would we receive for $ AUD? Conversion rate: So, we multiply by and get $ USD. 3

4 At today s rate, how many AUD would I receive for $350 USD? Here, we need to work out the conversion rate, so gives , which becomes our NEW conversion rate (our vice versa one). So, $350 USD = 350 x = $ AUD. Here are some for you to try. Using 1 AUD is worth EUR (Euros, ) and GBP (British Pounds, ), calculate what you would receive for the following conversions: 1. You want to convert $1 200 AUD to EUR 2. Converting $350 AUD to GBP 3. Convert GBP to AUD 4. Change 520 EUR to AUD Answers follow on the next page for you to check. If you need help with any of the Maths covered in this resource (or any other Maths topics), you can make an appointment with Learning Development through Reception: phone (02) , or Level 3 (top floor), Building 11, or through your campus. 4

5 ANSWERS 1. $1 200 AUD to EUR We know 1 AUD = EUR So, AUD = x EUR = EUR 2. $350 AUD to GBP 1 AUD = GBP So, 350 AUD = 350 x GBP = GBP GBP to AUD 1 AUD = GBP This means that 1 GBP = AUD = AUD (our new conversion rate) So, GBP = x AUD = AUD EUR to AUD 1 AUD = EUR So 1 EUR = AUD = AUD (our new conversion rate) So, 520 EUR = 520 x AUD = AUD 5

6 Measurement There are quite a few different types of conversions between measurements. One that we don t need so much these days but was very important in Australia a few years ago (when the Metric system was introduced) is to convert between one system of measurement and another. For example, you might find your grandmother s recipe book which contains measurements such as ounces and pounds (Imperial) but your scales are in grams and kilograms (Metric). Another kind of conversion is to express measurements in the Metric system as different units within that system. You might need to convert millimetres to metres, or grams to kilograms because your measuring device is not in the right units for what you want. A further kind of conversion concerns how the units, particularly in the Metric system, are equivalent, so that length, mass (weight) and volume (capacity) can all be linked together. This is really helpful especially for calculating water usage. We also need to convert between Fahrenheit ( F) and Celsius ( C) temperatures as some countries still use the Fahrenheit scale. This uses another different conversion method. Let s start with converting between systems. This is very similar to converting currencies (see the money section above). If we know the conversion factor, the method is very simple. The problem is to know all the conversion factors, but this is where the internet is very useful! Grandma s recipe calls for 8 ounces of mixed fruit. We need to convert this to grams. First, look for the conversion rate: 1 ounce = grams. So 8 ounces would be 8 x g g. Your scales are probably not that accurate so you would round this to 227 g, or even 225 or 230 g, depending on taste (or the amount of fruit you have available). Ounces Calculation Grams x ( 227) Source: 12/1/12 6

7 Another example: You may have been sewing for quite a long time, using a machine that has markings in inches, such as 5 " for a seam allowance. Now 8 you ve bought a new machine and need to work out what the seam allowance is in centimetres. (This calculation looks a bit tricky because it has fractions in it, but we can cope with that!) Firstly, what is the conversion rate? Internet time! 1 = 2.54 cm. So, we multiply 5 by If your calculator has fraction keys, this is not a problem; 8 however, if it doesn t, multiply 2.54 by 5 and divide the result by 8. Whichever way you calculate you should get Generally this is rounded DOWN to 1.5 cm (a little easier to work with than 1.6 cm). Here s one for you to try: A small seam allowance is ¼. Convert this to cm. Last example. You ve been watching the cricket and know that the length of the pitch is always referred to as 22 yards but wonder what this is in metres! Conversion factor: 1 yard = m. So, what is the length of the pitch? m, roughly 20 m You should get usually given as 0.6 cm Here are some more for you to try. You will need the following information: 1 inch = 2.54 cm 1 kg = 2.2 pounds 1 mile = 1.6 km 1 L = 0.22 gallons (UK) 7

8 Convert each of the following. You can check your answers on the next page inches to cm kg to pounds miles to km L to gallons (UK) cm to inches pounds to kg km to miles gallons (UK) to L If you need help with any of the Maths covered in this resource (or any other Maths topics), you can make an appointment with Learning Development through Reception: phone (02) , or Level 3 (top floor), Building 11, or through your campus. 8

9 Solutions to conversion (previous page) 1. 1 inch = 2.54 cm So, 5.7 inches = 5.7 x 2.54 cm = cm 2. 1kg = 2.2 pounds So, 78 kg = 78 x 2.2 pounds = pounds 3. 1 mile = 1.6 km So, 20 miles = 20 x 1.6 km = 32 km 4. 1 L = 0.22 gallons (UK) So, 30 L = 30 x 0.22 gallons (UK) = 6.6 gallons (UK) 5. 1 inch = 2.54 cm So, 1 cm = inches = inches So, 10 cm = 10 x inches = ( 4) inches 9

10 6. 1 kg = 2.2 pounds So, 1 pound = kg = 0.45 kg So, 150 pounds = 150 x 0.45 kg = ( 68) kg 7. 1 mile = 1.6 km So, 1 km = miles = miles So, 25 km = 25 x miles = ( 15.6) miles 8. 1 L = 0.22 gallons (UK) So, 1 gallon = L = 4.55 L So, 50 gallons (UK) = 50 x 4.55 L = ( 227) L 10

11 Converting within the Metric system mega M kilo k hecto h deca da U N I T. deci d centi c milli m In the Metric system, each prefix actually stands for a power of 10. For example, a kilometre is just metres, because the prefix kilo always means In the same way, a centigram is just 0.01 grams because centi always means 0.01 (or 1 ). This is the way that we can know the conversion 100 factors. There are many different ways of calculating when we need to convert between metric measurements. For example, we know that there are 10 millimetres in 1 centimetre. So, there must be 2 x 10 millimetres in 20 centimetres. Our conversion factor is 10. Between each column of the table of prefixes, the conversion factor is 10. If we want to go between two columns, the conversion factor must be 100 and so on. Example: litre (L) Calculation millilitre (ml) x This works for converting large measures to smaller ones. The trick is to go back the other way! You can work out the new conversion factor by dividing 1 by the old conversion factor (in this case, if we want to convert millilitres to litres, the new conversion factor would be = 0.001) then multiplying the amount we wish to change. This is actually the same as just dividing the amount we wish to change by the old conversion factor. Example: Change 495 millilitres to litres. 11

12 There are three columns from millilitres to litres, so the conversion factor, going from left to right would be We need to go right to left, so we either multiply by , or we divide by 1000, which gives the same result. You need to choose which way works best for you! Changing 495 millilitres to litres: 495 ml = 495 x L = L. Or: 495 ml = L = L Check your answer by asking yourself if it makes sense. Example: Change km to m. The first thing to ask is: should we get more or less than for our answer? km = x m = m. This does make sense because there are already metres in 1 kilometre so there are going to be many more than that in km! (You can also make the numbers simpler for example, how would you calculate the number of metres in 2 kilometres?) Example: Change kg to Mg. This time we will get a smaller answer. This is where you either multiply by , or you just divide by Whichever way you calculate, you should end up with 65.32Mg. 12

13 Here are some for you to try. You can check your answers on the next pages. 1. Change 5.3m to cm 2. Change 6.82kg to g 3. Change 180mm to cm 4. Change 9 567mg to g 5. Change 3.5L to ml 6. Change 1 483g to kg 7. Change kl to ML 8. Change 9ML to L If you need help with any of the Maths covered in this resource (or any other Maths topics), you can make an appointment with Learning Development through Reception: phone (02) , or Level 3 (top floor), Building 11, or through your campus. 13

14 Solutions to Converting within the Metric System 1. Change 5.3m to cm There are 2 columns from m to cm so the conversion factor must be 100. We are going from left to right, so we multiply by 100: 5.3m = 5.3 x 100 cm = 530cm 2. Change 6.82 km to m There are 3 columns from km to m and we are going from left to right, so we multiply by km = 6.82 x m = 6 820m 3. Change 180 mm to cm There is 1 column from mm to cm and we are going from right to left, so we divide by 10 (or we multiply by 1 10). 180mm = cm = 18cm 4. Change mm to m There are 3 columns from mm to m and we are going from right to left, so we divide by (or multiply by ) mm = m = 9.567m 14

15 5. Change 3.5 L to ml There are 3 columns from L to ml and we are going from left to right, so we multiply by L = 3.5 x ml = 3 500mL 6. Change g to kg There are 3 columns from g to kg and we are going from right to left, so we divide by (or multiply by ) g = kg = 1.483kg 7. Change kl to ML There are 3 columns from kl to ML and we are going from right to left, so we divide by kL = ML = 18ML 8. Change 9 ML to L There are 6 columns from ML to L and we are going from left to right, so we multiply by ML = 9 x L = L 15