Question

The following masses are given in kilograms. Use metric prefixes on the gram to rewrite them so the numerical value is bigger than one but less than 1000. For example, 7×10^{−4}kg could be written as 70 cg or 700 mg.

(a) 3.8×10^{−5} kg;
(b) 2.3×10¹⁷kg;
(c) 2.4×10^{−11}kg;
(d) 8×10¹⁵kg;
(e) 4.2×10^{−3}kg.

Answer 1

Masses given in kilograms are converted to grams using metric prefixes to yield numerical values between 1 and 1000. For example, 3.8 × 10^{-5} kg is 38 mg, and 2.3 × 10^{17} kg is 230 Pg.

Step-by-step explanation:

The task is to use metric prefixes so that the masses are rewritten with numerical values between 1 and 1000 when converted to grams.

1. 3.8 × 10^{-5} kg: This is equal to 38 milligrams (mg) since 1 kg = 1,000,000 mg.
2. 2.3 × 10^{17} kg: This massive number is equivalent to 230 petagrams (Pg) because 1 kg = 10^{-15} Pg.
3. 2.4 × 10^{-11} kg: This converts to 24 micrograms (μg) since 1 kg = 1,000,000,000,000 μg.
4. 8 × 10^{15} kg: This can be expressed as 8000 teragrams (Tg) because 1 kg = 10^{-12} Tg.
5. 4.2 × 10^{-3} kg: This is the same as 4200 milligrams (mg), given 1 kg = 1,000,000 mg.