Final answer:
To express measurements using prefix multipliers, you identify the nearest metric prefix that corresponds to the power of ten in the given values. Measurements are then expressed in megagrams (Mg), angstroms, teragrams (Tg), and micrograms (μg) to avoid using exponents.
Step-by-step explanation:
To express each measurement using prefix multipliers without exponents, you must identify the appropriate metric prefix that corresponds to the power of ten given. Here's how you convert each value:
A. 35.6×10⁵ g: 'Mega-' represents 10⁶, so closer but less than this is 10⁵, which means we can express it as 3.56 Mg (megagrams) because 35.6×10⁵ g = 3.56×10⁶ g.
B. 17.7×10⁻¹⁰ g: 'Angstrom' is often used for 10⁻¹⁰, so it can be expressed as 177 angstroms since 1 g = 10⁻± angstroms.
C. 36.7×10¹¹ g: 'Tera-' represents 10¹¹, so we can express it as 36.7 Tg (teragrams) since 36.7×10¹¹ g = 36.7×10¹¹ g.
D. 87.8×10⁻⁷ g: 'Micro-' represents 10⁻⁶, so closer but more than this is 10⁻⁷, which means we can write it as 878 μg (micrograms) since 87.8×10⁻⁷ g = 878×10⁻⁶ g.
It's important to choose the most practical and easiest to manage unit, which often means keeping the numerical value between one and 1000 when possible.