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

Converting larger units of length into smaller units of length:

Examples:

1. Convert 22 cm to mm.

Solution:

We know that 1 cm = 10 mm

22 cm = 22 × 10 mm

= 220 mm

2. Convert 17 cm 8 mm to mm.

Solution:

17 cm 8 mm = 17 cm + 8 mm

We know that 1 cm = 10 mm

17 cm + 8 mm = 17 × 10 mm + 8 mm

= 170 mm + 8 mm

= 178 mm

3. Convert 5 km to meters. Solution:

We know that 1 km = 1000 m

5 km = 5 × 1000 m

= 5000 m

4th Convert 9 km 248 m to meters

Solution:

9 km 248 m = 9 km + 248 m

We know that 1 km = 1000 m

9 km + 248 m = 9 × 1000 m + 248 m

= 9000 m + 248 m

= 9248 m

5. Convert 4 meters to decimeters.

Solution:

We know that 1 m = 10 dm

4 m = 4 × 10 dm

= 40 dm

Conversion of larger mass units into smaller mass units:

To convert kilograms to grams and grams to milligrams, we multiply by 1000.

For example:

1. Convert 5 g to mg.

We know that 1 g = 1000 mg

5 g = 5 x 1000 mg

= 5000 mg

2. 5 kg express 350 g as g.

We know that 1 kg = 1000 g

So, 5 kg = 5 × 1000 g

= 5000 g

5 kg 350 g = 5000 g + 350 g

= 5300 g

Convert larger capacity units into smaller capacity units:

To convert liters to milliliters, we multiply the number of liters by 1000.

For example:

1. Express 54 l in ml.

We know that 1 l = 1000 ml

Hence 54 l = 54 × 1000 ml

= 54000 ml

2. 29 l express 360 ml in ml.

We know that 1 l = 1000 ml

So 29 l 360 ml = 29 × 1000 ml + 360 ml

= 29000 ml + 360 ml

= 29360 ml

Solved examples for converting larger units into smaller units:

1. Convert 723,469 kilograms to the following units:

(i) hectograms

(ii) decagrams

(iii) grams

(iv) decigrams

(v) centigrams

(vi) milligrams

Solution:

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

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

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

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

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

(vi) 723.469 kg = (723.469 x 1,000,000) mg = 723469,000 mg

Let’s look at another example with 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 in 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 in 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

3. Convert 9 m 8 dm to decimeters.

Solution:

9 m 8 dm = 9 m + 8 dm

We know that 1 m = 10 dm

9 m + 8 dm = 9 × 10 dm + 8 dm

= 90 dm + 8 dm

= 98 dm

Questions and answers about larger units about smaller units:

I. Convert the given lengths from cm to mm:

(i) 6 cm = ………… .. mm

(ii) 35 cm = ………… .. mm

(iii) 12 cm = ………… .. mm

(iv) 62 cm = ………… .. mm

(v) 20 cm = ………… .. mm

(vi) 102 cm = ………… .. mm

(vii) 23 cm = ………… .. mm

(viii) 150 cm = ………… .. mm Reply:

I. (i) 60 mm

(ii) 350 mm

(iii) 120 mm

(iv) 620 mm

(v) 200 mm

(vi) 1020 mm

(vii) 230 mm

(viii) 1500 mm

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