Unit Conversions

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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

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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