☰ خطة العام · الرياضيات (بالإنجليزية)

Multiplying decimals to thousandths and the metric system

الأسبوع 10 · ضرب الكسور العشرية حتى الأجزاء من ألف والنظام المتري · 3 دروس
3

Metric units, powers of ten and multistep decimal stories

Discover Mathematics P5: Term 1, Unit 5, Lessons 5–10
GoalChange between metric units with powers of ten and solve multistep stories with decimals.
New words
kilometre (km) · 1 km = 1,000 mmillilitre (mL) · 1 L = 1,000 mLconvert · to rewrite a measure in another unit
Explanation

The metric system is built on powers of ten, so converting units is the same as moving digits. To change a larger unit to a smaller one, multiply: 1 km = 1,000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1,000 g and 1 L = 1,000 mL. So 3.25 km = 3.25 × 1,000 = 3,250 m and 0.75 L = 0.75 × 1,000 = 750 mL. To change a smaller unit to a larger one, the digits move the other way (to the right): 350 g is 0.35 kg. For a multistep story, convert everything to one unit first, then calculate, and give the answer in a sensible unit.

Bigger unitSmaller unitMultiply by
1 km1,000 m1,000
1 m100 cm100
1 cm10 mm10
1 kg1,000 g1,000
1 L1,000 mL1,000
Worked examples
A path is 3.25 km long. In metres: 3.25 × 1,000 = 3,250 m. A bottle holds 0.75 L. In millilitres: 0.75 × 1,000 = 750 mL. In both cases the digits move three places left.
Add 1.8 m and 45 cm. Change to one unit first: 1.8 m = 1.8 × 100 = 180 cm. Then 180 + 45 = 225 cm, which is 2.25 m.
Hana bakes 14 cakes for a school fair, using 0.25 kg of flour for each. Flour: 0.25 × 14 = 3.5 kg, which is 3.5 × 1,000 = 3,500 g. Flour is sold in 1 kg bags at 22.5 LE. She needs 4 bags, because 3 bags are only 3 kg. Cost: 4 × 22.5 = 90 LE.
Class activity

Kitchen conversions. Find three packages at home with a mass or volume written on the label in g, kg, mL or L. Write each one in two units, for example 0.5 kg = 500 g. Then pick two packages and add them in the smaller unit. Say how many kilograms or litres the total is.

Practice
1
Change 2.5 km to metres.
2
Change 0.4 L to millilitres.
3
Change 1.35 m to centimetres.
4
Change 350 g to kilograms.
5
A path is 0.85 km long. Marwan walks along it 12 times. How far does he walk in km and in m?