All 15 Free Lessons

The Metric System

Free preview: one of our 15 free lessons, the first lesson of each topic. No account needed.

Video Lesson

Ready to check your understanding?

Take the short multiple-choice test. If you need more help, review the written lesson and worked examples below.

You can pause, replay or use the written lesson below to review at any time.

Written Lesson

The metric system is the main system of measurement used in CSEC Mathematics. It is based on powers of 10, so converting between units is usually done by multiplying or dividing by 10, 100, or 1000.

What You Will Learn

  • Recognise the main metric units, including temperature
  • Write metric unit symbols correctly
  • Understand common metric prefixes
  • Choose an appropriate unit for a measurement
  • Convert between larger and smaller metric units
  • Complete multi-step and two-unit conversions
  • Convert square and cubic units
  • Use common metric and imperial approximations
  • Solve practical measurement problems

Key Ideas

  • The metre is used to measure length.
  • The gram is used to measure mass.
  • The litre is used to measure capacity or volume of liquid.
  • The degree Celsius is used to measure everyday temperature.
  • Kilo means 1000 times the base unit.
  • Centi means one hundredth of the base unit.
  • Milli means one thousandth of the base unit.

Common Metric Units

Measurement Base Unit Common Units
Length metre, m km, m, cm, mm
Mass gram, g kg, g, mg
Capacity litre, L L, mL
Temperature degree Celsius, °C °C

Writing Metric Symbols Correctly

Metric symbols are case-sensitive. Capital and lowercase letters cannot be swapped.

  • Write mL, not ml. The capital L avoids confusion with the number 1.
  • Write km and kg in lowercase.
  • Write °C for degrees Celsius.
  • Leave a space between the number and the unit: 8 kg, not 8kg.
  • Do not add an "s" to make a symbol plural: 5 km, not 5 kms.

Metric Prefixes

Prefix Symbol Meaning Value
kilo k one thousand 1000
hecto h one hundred 100
deca da ten 10
basic unit — one 1
deci d one tenth 0.1
centi c one hundredth 0.01
milli m one thousandth 0.001

The most commonly used prefixes in everyday measurements are kilo, centi and milli.

Choosing an Appropriate Unit

Before measuring something, think about how big or small it is. This helps you choose a sensible unit.

Measurement Appropriate Unit
Thickness of a coinmillimetres
Length of a pencilcentimetres
Height of a doormetres
Distance between townskilometres
Mass of a tabletmilligrams
Mass of a loaf of breadgrams
Mass of a personkilograms
Medicine in a spoonmillilitres
Water in a large bottlelitres

How to Convert Metric Units

  • When changing from a larger unit to a smaller unit, multiply.
  • When changing from a smaller unit to a larger unit, divide.
Larger unit → smaller unit: multiply
Smaller unit → larger unit: divide

Useful Conversions to Remember

  • 1 km = 1000 m
  • 1 m = 100 cm
  • 1 m = 1000 mm
  • 1 kg = 1000 g
  • 1 g = 1000 mg
  • 1 L = 1000 mL

Worked Examples

Example 1: Convert 3 km to metres.

  1. We are changing from kilometres to metres.
  2. Kilometres are larger than metres.
  3. So we multiply by 1000.
  4. 3 × 1000 = 3000

Answer: 3000 m

Example 2: Convert 250 cm to metres.

  1. We are changing from centimetres to metres.
  2. Centimetres are smaller than metres.
  3. So we divide by 100.
  4. 250 ÷ 100 = 2.5

Answer: 2.5 m

Example 3: Convert 0.4 m to centimetres.

  1. We are changing from metres to centimetres.
  2. Metres are larger than centimetres.
  3. So we multiply by 100.
  4. 0.4 × 100 = 40

Answer: 40 cm

Example 4: Convert 5 kg to grams.

  1. We are changing from kilograms to grams.
  2. Kilograms are larger than grams.
  3. So we multiply by 1000.
  4. 5 × 1000 = 5000

Answer: 5000 g

Example 5: Convert 3 m 45 cm entirely to centimetres.

  1. A measurement with two units must first be split into one unit.
  2. Change the metres to centimetres: 3 × 100 = 300 cm.
  3. Add the extra centimetres: 300 + 45 = 345.

Answer: 345 cm

Example 6: Convert 0.045 km to centimetres.

  1. There is no direct km-to-cm fact to remember, so we convert in two steps.
  2. First change km to m: 0.045 × 1000 = 45 m.
  3. Then change m to cm: 45 × 100 = 4500.

Answer: 4500 cm

Example 7: Which is longer, 2.4 m or 235 cm?

  1. Before comparing, both measurements must be in the same unit.
  2. Change 2.4 m to centimetres: 2.4 × 100 = 240 cm.
  3. Compare: 240 cm is greater than 235 cm.

Answer: 2.4 m is longer.

Example 8: Convert 2.5 m² to square centimetres.

  1. Square units need the conversion factor squared, not just multiplied once.
  2. Since 1 m = 100 cm, 1 m² = 100 × 100 = 10 000 cm².
  3. 2.5 × 10 000 = 25 000.

Answer: 25 000 cm²

Example 9: Express 3.2 L in cubic centimetres.

  1. Remember that 1 L = 1000 cm³, and also that 1 mL = 1 cm³.
  2. 3.2 × 1000 = 3200.

Answer: 3200 cm³

Example 10: Convert 40 km to miles, using 5 miles ≈ 8 km.

  1. Imperial-to-metric relationships are approximate, so we use ≈, not =.
  2. Find how many groups of 8 km are in 40 km: 40 ÷ 8 = 5.
  3. Multiply by 5 miles: 5 × 5 = 25.

Answer: 40 km ≈ 25 miles

Example 11: A container holds 1.5 L of juice, poured into glasses that each hold 200 mL. How many glasses can be filled completely, and how much juice remains?

  1. Change litres to millilitres first: 1.5 × 1000 = 1500 mL.
  2. Divide by the capacity of one glass: 1500 ÷ 200 = 7 remainder 100.
  3. Only the whole-number part counts as a full glass. The remainder is the juice left over.

Answer: 7 full glasses, with 100 mL remaining.

Important Reminder

If the unit is getting smaller, the number gets bigger. If the unit is getting bigger, the number gets smaller.

Common Mistakes

1. Multiplying in the wrong direction. Multiply for larger-to-smaller, divide for smaller-to-larger. Mixing these up gives an answer that is far too big or far too small.
2. Squaring the wrong number. Since 1 m = 100 cm, it is tempting to write 1 m² = 100 cm². This is wrong. Square the conversion factor: 1 m² = 100² cm² = 10 000 cm².
3. Confusing litres and cubic centimetres. 1 mL = 1 cm³, but 1 L = 1000 cm³, not 1 cm³.
4. Rounding up full containers. A result like 7.5 glasses means 7 full glasses, not 8. Do not round the number of complete containers up.

Lesson Summary

  • The metric system is based on powers of 10.
  • Metric symbols are case-sensitive: write mL, L, and °C correctly.
  • Kilo means ×1000, centi means ÷100, milli means ÷1000.
  • Multiply when converting a larger unit to a smaller unit. Divide the other way.
  • Two-unit measurements and multi-step conversions are solved by converting to one unit at a time.
  • Convert measurements to the same unit before comparing or calculating with them.
  • Square the conversion factor for area units. It stays the same value for capacity: 1 mL = 1 cm³.
  • Imperial-to-metric conversions are approximate, shown with ≈.
  • For full-container problems, use only the whole-number result and find the remainder separately.

Practice Questions

  1. 1. How many metres are in 5 km?
  2. 2. Convert 0.4 m to centimetres.
  3. 3. Convert 750 cm to metres.
  4. 4. Convert 2.5 kg to grams.
  5. 5. Convert 3000 mL to litres.
  6. 6. Write the correct symbol for millilitre.
  7. 7. Convert 4 m 20 cm entirely to centimetres.
  8. 8. Convert 0.06 km to centimetres.
  9. 9. Which is longer, 3.1 m or 305 cm?
  10. 10. Convert 1.8 m² to square centimetres.
  11. 11. Express 4.5 L in cubic centimetres.
  12. 12. Convert 16 km to miles, using 5 miles ≈ 8 km.
  13. 13. A container holds 2 L of juice, poured into 250 mL cups. How many cups can be filled completely, and how much juice remains?
  14. 14. Write the prefixes kilo, centi, and milli as their meanings.

Answers

  1. 5000 m
  2. 40 cm
  3. 7.5 m
  4. 2500 g
  5. 3 L
  6. mL
  7. 420 cm
  8. 6000 cm
  9. 3.1 m is longer (310 cm > 305 cm)
  10. 18 000 cm²
  11. 4500 cm³
  12. 10 miles
  13. 8 full cups, with no juice remaining
  14. kilo = one thousand, centi = one hundredth, milli = one thousandth

Finished reviewing the lesson?

Take the multiple-choice test to check your understanding and complete this lesson.

What would you like to do next?

Try the first lesson of another course, or unlock every lesson for US$49 for one full year.

Try Another Free LessonGet Full Access