To convert a bigger unit a smaller unit, we move the decimal point of the right. In other words, we can say that we multiply. This is very important for us to learn how to convert bigger units into smaller units. We use it often in our daily life.

**Solved examples for the conversion of bigger units to smaller units:**

**1.** Convert 723.469 kilograms into the following units:

(i) hectograms

(ii) decagrams

(iii) grams

(iv) decigrams

(v) centigrams

(vi) milligrams

**Solution:**

(i) 723.469 kg = (723.469 × 10) hg = 7234.69 hg

(ii) 723.469 kg = (723.469 × 100) dag = 72346.9 dag

(iii) 723.469 kg = (723.469 × 1000) g = 723469 g

(iv) 723.469 kg = (723.469 × 10000) dg = 7234690 dg

(v) 723.469 kg = (723.469 × 100000) cg = 72346900 cg

(vi) 723.469 kg = (723.469 × 1000000) mg = 723469000 mg

Let us consider another example involving different types of conversions.

**2.** Convert the following:

(i) 8 m 6 dm 3 cm 2 mm to mm

(ii) 2 kg 4 hg 6 dag 8 g to g

(iii) 7 l 1 dl 4 cl 9 ml to ml

**Solution:**

(i) 8 m 6 dm 3 cm 2 mm to mm

= (8 × 1000 + 6 × 100 + 3 × 10 + 2) mm, [Because 1 m = 1000 mm, 1 dm = 100 mm and 1 cm = 10 mm]

= (8000 + 600 + 30 + 2) mm

= 8632 mm

(ii) 2 kg 4 hg 6 dag 8 g to g

= (2 × 1000 + 4 × 100 + 6 × 10 + 8) g, [Because 1 kg = 1000 g, 1 dg = 100 g and 1 dag = 10 g]

= (2000 + 400 + 60 + 8) g

= 2468 g

(iii) 7 l 1 dl 4 cl 9 ml to ml

= (7 × 1000 + 1 × 100 + 4 × 10 + 9) ml, [Because 1 l = 1000 ml, 1 dl = 100 ml and 1 cl = 10 ml]

= (7000 + 100 + 40 + 9) g

= 7149 ml

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