Year 11 Exam>Year 11 Notes>Unit Conversions
Table of contents | |
Unit Conversions (CIE IGCSE Maths: Extended) | |
Revision Note | |
Converting Units | |
Converting Units of Length | |
Unit Conversions for Metric Units | |
Unit Conversions for Volume/Capacity | |
Converting Weights | |
Understanding Unit Conversions and Cubed Units | |
Understanding Volume Conversions | |
Unit Conversions |
Unit Conversions (CIE IGCSE Maths: Extended)
Revision Note
Author
Expertise
Maths
Converting Units
How to Convert Units for Lengths
- Conversion of metric units involves multiplying or dividing by powers of 10.
- Basic conversions to remember:
- 1 cm = 10 mm
- 1 m = 100 cm
- 1 km = 1000 m
- To decide whether to multiply or divide, consider if the number of units increases or decreases.
- Example: Since the number of mm is 10 times greater than cm, mm = cm × 10.
- You can perform conversions in stages. For example, convert kilometers to meters, then meters to centimeters.
- When given an imperial conversion (e.g., miles to kilometers), ratios can be used for conversions.
- Example: There are 5 miles in 8 kilometers. To find how many miles are in 13 kilometers, solve using ratios.
Converting Units of Length
- 1 cm = 10 mm
- 1 m = 100 cm
- 1 km = 1000 m
- To decide whether to multiply or divide, consider if the number of units increases or decreases. For example, since the number of mm is 10 times greater than cm, mm = cm x 10.
- You can perform conversions in stages. Start by converting kilometres into metres, and then metres into centimetres.
- If you encounter an imperial conversion (e.g., miles to kilometres), you can use ratios for assistance. For instance, if there are 5 miles in 8 kilometres, you can determine how many miles are in 13 kilometres by solving the ratio.
How do I convert units for mass?
- Paraphrase the information provided, explaining with examples where necessary.
- Convey all points in bullet format with appropriate headings.
- Ensure no more than 2 headings are in H7 format and no more than 4 subheadings are in H8 format; otherwise, make the headings bold.
- Keep the language simple to understand and provide detailed explanations.
Unit Conversions for Metric Units
- Conversion of metric units involves multiplying or dividing by powers of 10.
- Understanding basic conversions is key:
- 1 gram (g) = 1000 milligrams (mg)
- 1 kilogram (kg) = 1000 grams (g)
- 1 tonne = 1000 kilograms (kg)
- Imperial conversions, like pounds to kilograms, can be solved using ratios.
- For example, with 2.2 pounds in 1 kilogram, to convert 10 pounds to kilograms, you'd calculate accordingly.
Examples:
Converting 500 grams to kilograms: 500 g * (1 kg / 1000 g) = 0.5 kg
Converting 3 tonnes to grams: 3 tonnes * 1000 kg/tonne * 1000 g/kg = 3,000,000 grams
Unit Conversions for Volume/Capacity
- For metric units, conversion entails multiplying or dividing by powers of 10.
- Essential conversions to remember:
- 1 liter (l) = 1000 milliliters (ml)
- 1 centiliter (cl) = 10 milliliters (ml)
- 1 milliliter (ml) = 1 cubic centimeter (cm3)
- Imperial conversions, such as pints to liters, can be tackled with ratios.
- For instance, 1.75 pints in 1 liter means to find how many liters are in 5 pints, you'd apply the appropriate ratio.
Examples:
Converting 2500 milliliters to liters: 2500 ml * (1 l / 1000 ml) = 2.5 liters
Converting 4 centiliters to cubic centimeters: 4 cl * 10 ml/cl * 1 cm3/ml = 40 cm3
How do I convert units for volume/capacity?
Converting Units
- Converting from centimeters to millimeters:
- When converting 54 cm to mm, remember that 1 cm is equal to 10 mm. Therefore, 54 cm is equal to 540 mm.
- Result: 540 mm
Converting from centimeters to kilometers
- First, convert 12,300 cm to meters:
- Since 100 cm is equal to 1 m, 12,300 cm is equal to 123 m.
- Next, convert 123 m to kilometers:
- Given that 1000 m is equal to 1 km, 123 m is equal to 0.123 km.
- Result: 0.123 km
Converting Weights
- Converting 485 grams to kilograms:
- Knowing that 1000 g is equivalent to 1 kg, 485 g is equal to 0.485 kg.
- Result: 0.485 kg
Squared & Cubic Units
- Converting between squared units, commonly used for areas, requires special attention. Remember to square the conversion rates because area is two-dimensional. The presence of "squared" in the units can serve as a helpful reminder of this concept.
- Basic conversion examples include:
- 1 cm2 = 102 mm2 = 100 mm2
- 1 m2 = 1002 cm2 = 10,000 cm2
- 1 km2 = 1,0002 m2 = 1,000,000 m2
- For less common conversions, remember:
- 1 hectare (ha) = 10,000 m2
Additional Guidelines:
- When dealing with imperial conversions for lengths, such as miles to kilometers:
- Express the conversion as a ratio (e.g., Miles to kilometers is 5:8)
- Square the numbers to obtain the ratio for area unit conversion (e.g., Miles2 to kilometers2 is 25:64)
Understanding Unit Conversions and Cubed Units
- 1 hectare (ha) = 10,000 m2
- If you are given an imperial conversion (such as miles to kilometers) for lengths, write the conversion as a ratio. For example, Miles to kilometers is 5 : 8. Square the numbers to get the ratio for the conversion of the units for area. For instance, Miles^2 to kilometers^2 is 25 : 64.
- How do I convert between cubed units?
Converting Length Units
- Write the conversion as a ratio, e.g., Miles to kilometers is 5 : 8.
Converting Area Units
- Square the numbers to get the ratio for the conversion of the units for area. For example, Miles^2 to kilometers^2 is 25 : 64.
Understanding Volume Conversions
- Cubing Conversion Rates:
- When converting units for volume, it's essential to cube the normal conversion rates. This is because volume is three-dimensional, and the units being cubed help in remembering this concept.
- Basic Conversions:
- 1 cm^3 = 10^3 mm^3 = 1000 mm^3
- 1 m^3 = 100^3 cm^3 = 1,000,000 cm^3
- 1 km^3 = 1000^3 m^3 = 1,000,000,000 m^3
- Imperial Conversions for Lengths:
- When dealing with imperial conversions like miles to kilometers for lengths, write the conversion as a ratio (e.g., 5:8).
- To convert the units for volume, cube the numbers in the ratio. For example, converting miles^3 to kilometers^3 would be 125:512.
Converting Area Units
- Converting 8254 mm^2 to cm^2:
- Given: 10 mm = 1 cm
- Calculate: 8254 mm^2 = (8254 ÷ 100) cm^2 = 82.54 cm^2
Unit Conversions
- Conversion of Cubic Meters to Cubic Centimeters
- 1 meter (m) = 100 centimeters (cm)
- 1 cubic meter (m^3) = 1,000,000 cubic centimeters (cm^3)
- 2.54 cubic meters (m^3) = (2.54 x 1,000,000) cm^3 = 2,540,000 cm^3
- Understanding the Conversion
- 2.54 cubic meters is equal to 2,540,000 cubic centimeters
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