2
Converting metric units with a conversion factor
Discover Mathematics P6: Term 2, Unit 10, Lessons 4–6
GoalConvert lengths, masses and capacities by multiplying by the factor that cancels the old unit.
New words
convert · to write the same amount in a different unitcancel · when the same unit is on top and at the bottom of a fraction, it disappearsestimate · to find about how big the answer should be before calculating
Explanation
To convert, multiply by a conversion factor written so that the OLD unit is at the bottom. The old unit cancels and the NEW unit is left. To change 4.5 km into metres, write 4.5 km × 1,000 m / 1 km. The km cancels and 4.5 × 1,000 = 4,500 m. To change 2,500 g into kg, write 2,500 g × 1 kg / 1,000 g = 2.5 kg. Always check the size of the answer. A smaller unit needs more of itself, so the number gets bigger (km to m, kg to g). A larger unit needs fewer, so the number gets smaller (g to kg, cm to m).
★Remember
Multiply by the factor with the OLD unit at the bottom. To a smaller unit the number grows; to a larger unit the number shrinks.
Worked examples
ƒFormula
4.5 km × 1,000 m / 1 km = 4,500 m
Change 2,500 g into kilograms. 2,500 g × 1 kg / 1,000 g = 2.5 kg. The kilogram is larger, so the number shrank. The same method gives 350 cm = 350 × 1 m / 100 cm = 3.5 m.
Change 1.2 L into millilitres: 1.2 × 1,000 = 1,200 mL. Change 36 mm into centimetres: 36 ÷ 10 = 3.6 cm. Before calculating, estimate: 1.2 L is a bit more than 1 L, so a bit more than 1,000 mL is right.
Class activity
Measure and convert. With a grown-up, measure the height of a door in cm and then write it in metres. Weigh a bag of sugar or rice in kg and write it in grams. Which number is bigger each time, and why?
Practice
1
Change 7 m into centimetres.
7 × 100 = 700 cm.
2
Change 8,000 g into kilograms.
8,000 ÷ 1,000 = 8 kg.
3
Change 0.75 L into millilitres.
0.75 × 1,000 = 750 mL.
4
Change 450 cm into metres.
450 ÷ 100 = 4.5 m.
5
A bag holds 2.4 kg of flour. How many grams is that? Is your number bigger or smaller than 2.4, and why?
2.4 × 1,000 = 2,400 g. It is bigger, because the gram is a smaller unit.