Discover Mathematics P6: Term 2, Unit 10, Lessons 4–6
GoalExplain what a conversion factor is and write one for two metric units.
New words
conversion factor · a ratio of two equal measures in different units, such as 100 cm : 1 mequal measures · two ways of writing the same length, mass or time, such as 1 kg and 1,000 gunit · the name of what we measure with, such as cm, kg or hour
Explanation
1 cm and 10 mm are the same length, so we can write the ratio 10 mm : 1 cm. A ratio of two equal measures in different units is a conversion factor. Because the two parts are equal, the fraction 10 mm / 1 cm is equal to 1. Multiplying a measure by a fraction equal to 1 does not change how much there is; it only changes the unit we use to say it. The same idea works for every pair of metric units: 100 cm : 1 m, 1,000 m : 1 km, 1,000 g : 1 kg, 1,000 mL : 1 L. For time it is 60 min : 1 h. Each factor can be turned upside down (1 m : 100 cm) and it is still a ratio of equal measures.
Pair of units
Conversion factor
Same as 1
mm and cm
10 mm : 1 cm
10 mm / 1 cm = 1
cm and m
100 cm : 1 m
100 cm / 1 m = 1
m and km
1,000 m : 1 km
1,000 m / 1 km = 1
g and kg
1,000 g : 1 kg
1,000 g / 1 kg = 1
mL and L
1,000 mL : 1 L
1,000 mL / 1 L = 1
min and h
60 min : 1 h
60 min / 1 h = 1
Worked examples
Metres
1
2
0.5
Centimetres
100
200
50
A ribbon is 1 m long. In centimetres it is 100 cm. The conversion factor is 100 cm : 1 m. Half a metre is 50 cm and two metres are 200 cm: the same factor works for any number of metres.
Is 1,000 m : 1 km a conversion factor? Yes: 1 km is exactly 1,000 m. Is 100 m : 1 km one? No, because 100 m is not equal to 1 km. A conversion factor must join two measures that are really equal.
Time has a conversion factor too. 1 hour is 60 minutes, so the factor is 60 min : 1 h. Then 2 h = 2 × 60 = 120 min.
Class activity
Factor cards. On small cards write the pairs of units you know (mm and cm, m and km, g and kg, mL and L). On the back write the conversion factor. Ask someone to show the front; you say the factor.
Practice
1
Write the conversion factor for kilometres and metres.
1,000 m : 1 km.
2
Write the conversion factor for kilograms and grams.
1,000 g : 1 kg.
3
Write the conversion factor for litres and millilitres.
1,000 mL : 1 L.
4
Is 10 cm : 1 m a conversion factor? Explain.
No. 1 m is 100 cm, not 10 cm, so the two parts are not equal. The factor is 100 cm : 1 m.
5
Write the factor for days and hours (1 day = 24 hours).
