Final answer:
Metric prefixes can be rewritten as powers of ten in scientific notation by replacing the prefix with the appropriate exponent. For the given lengths, they can be respectively converted to 89 × 1012 m, 89 × 10-12 m, 711 × 10-3 m, and 0.45 × 10-6 m.
Step-by-step explanation:
The metric prefixes are a way to express large and small numbers in a more manageable form using powers of ten. When we wish to rewrite these lengths without the prefix in scientific notation, we must represent them with their corresponding power of ten. The conversion involves just replacing the prefix with the actual power of ten it signifies. Let's now convert each given length:
- (a) The prefix 'T' (tera-) stands for 1012, so 89 Tm (terameters) is written as 89 × 1012 m.
- (b) The prefix 'p' (pico-) stands for 10-12, so 89 pm (picometers) is written as 89 × 10-12 m.
- (c) The prefix 'm' (milli-) stands for 10-3, so 711 mm (millimeters) is written as 711 × 10-3 m.
- (d) The prefix 'μ' (micro-) stands for 10-6, so 0.45μm (micrometers) is written as 0.45 × 10-6 m.
The conversions then become:
- (a) 89 Tm = 89 × 1012 m
- (b) 89 pm = 89 × 10-12 m
- (c) 711 mm = 711 × 10-3 m
- (d) 0.45μm = 0.45 × 10-6 m