For measurements of volume: To obtain the next largest multiple, divide it by 1 000. For example: 4 000 dm3 = 4 m3. To obtain the next smallest submultiple, multiply it by 1 000. For example: 2 hm3 = 2 000 dam3. What do the factors in the table mean? Volume km3 hm3 dam3 m3 dm3 cm3 mm3 : 1 000 : 1 000 : 1 000 : 1 000 : 1 000 : 1 000 × 1 000 × 1 000 × 1 000 × 1 000 × 1 000 × 1 000 Multiples 103 = 1 000 106 = 1 000 000 109 = 1 000 000 000 thousand million thousand million 3 zeros 6 zeros 9 zeros Submultiples 10-3 = 1 103 = 0.001 10-6 = 1 106 = 0.000 001 10-9 = 1 109 = 0.000 000 001 thousandth millionth thousand millionth 3 zeros 6 zeros 9 zeros Name Symbol Factor Unit Multiple kilo k × 109 km3 hecto h × 106 hm3 deca da × 103 dam3 Base unit m3 Submultiple deci d × 10-3 dm3 centi c × 10-6 cm3 milli m × 10-9 mm3 S O LV E D P R O B L E M 5 Write 0.5 m3 in mm3. 1. Identify the units. m3 ® mm3 2. To move from one to the other, go towards the submultiples. The exponent of 1 000 will be positive. 3. Count the number of steps between the two units. This is the exponent of 1 000. m3 dm3 cm3 mm3 4. Write it in the corresponding unit. 0.5 m3 = 0.5 × 1 0003 mm3 = 0.5 · 109 mm3 = = 500 000 000 mm3 S O LV E D P R O B L E M 6 Write 850 dam3 in km3. 1. Identify the units. dam3 ® km3 2. To move from one to the other, go towards the multiples. The exponent of 1 000 will be negative. 3. Count the number of steps between the two units. This is the exponent of 1 000. km3 hm3 dam3 4. Write it in the corresponding unit. 850 dam3 = 850 × 1 000-2 km3 = 850 × 10-6 km3 = = 850 × 1 106 km3 = 0.000 85 km3 × 1 000 × 1 000 × 1 000 3 steps : 1 000 : 1 000 2 steps 24 Convert these amounts: a) 73.357 cm3 ® mm3 b) 1.0576 dam3 ® dm3 25 Order these amounts from largest to smallest: 6.42 cm3 0.935 dm3 2 575 mm3 A C T I V I T I E S 2.4. Volume Volume is a quantity obtained by multiplying three lengths, which must be expressed in the same unit. For example: 5.40 m × 6.50 m × 3.0 m = 105.3 m3 2. Measurement 18
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