Final answer:
To arrange the given lengths in ascending order, convert them all to the same unit (millimeters). The ascending order is 27 am, 280 mm, and 0.3 m. Using metric prefixes, 7.59 × 107m is 75.9 Mm, 0.0074 m is 7.4 mm, 8.8 × 10-11 m is 88 pm, and 1.63 x 1013 m is 16.3 Tm.
Step-by-step explanation:
The student is asked to arrange the following lengths in ascending order: 27 am, 0.3 m, 280 mm. To compare these values, they must first be converted to the same unit. One meter (m) is equal to 1000 millimeters (mm), and an attometer (am) is much smaller than a meter, with 1 am being equal to 10-18 meters. Converting all lengths to millimeters, we get:
- 27 am = 27 × 10-18 × 1000 mm = 2.7 × 10-14 mm
- 0.3 m = 0.3 × 1000 mm = 300 mm
- 280 mm = 280 mm (no conversion needed)
So, the lengths in ascending order are: 27 am, 280 mm, 0.3 m.
Additionally, using metric prefixes to rewrite the given lengths so the numerical value is bigger than one but less than 1000:
- 7.59 × 107m can be written as 75.9 Mm (megameters).
- 0.0074 m can be written as 7.4 mm (millimeters).
- 8.8 × 10-11 m can be written as 88 pm (picometers).
- 1.63 x 1013 m can be written as 16.3 Tm (terameters).