- Convert all values to decimal format to compare them accurately.
- Order the first set from least to greatest: \(-17 \frac{1}{2}, -6, 40\%, 73\%, \frac{27}{10}, 22.18\).
- Order the temperatures from greatest to least: \(130^\circ\text{F}, 80^\circ\text{F}, 35^\circ\text{F}, 0^\circ\text{F}, -15^\circ\text{F}, -60^\circ\text{F}\).
- The ordered results are:
- Part 7: \(\boxed{-17 \frac{1}{2}, -6, 40\%, 73\%, \frac{27}{10}, 22.18}\)
- Part 8b: \(\boxed{130^\circ\text{F}, 80^\circ\text{F}, 35^\circ\text{F}, 0^\circ\text{F}, -15^\circ\text{F}, -60^\circ\text{F}}\)
Explanation
- Ordering the set of numbers from least to greatest
To order the given set of numbers, we first convert all values to decimal format for consistent comparison:
- \(73\% = \frac{73}{100} = 0.73\)
- \(22.18 = 22.18\)
- \(-17 \frac{1}{2} = -17.5\)
- \(-6 = -6\)
- \(40\% = \frac{40}{100} = 0.40\)
- \(\frac{27}{10} = 2.7\)
Now, list these values: \(\{0.73, 22.18, -17.5, -6, 0.40, 2.7\}\). Ordering them from least (most negative) to greatest (most positive), we get:
\(-17.5 < -6 < 0.40 < 0.73 < 2.7 < 22.18\).
Mapping these back to their original forms:
\(-17 \frac{1}{2}, -6, 40\%, 73\%, \frac{27}{10}, 22.18\).
- Working with temperatures
We are given the temperatures: \(130^\circ\text{F}, -15^\circ\text{F}, -60^\circ\text{F}, 80^\circ\text{F}, 35^\circ\text{F}, 0^\circ\text{F}\).
AOn a standard vertical thermometer, values are plotted such that higher values are positioned above lower values. The order from lowest to highest is \(-60, -15, 0, 35, 80, 130\).
BTo order these from greatest to least, we simply sort them in descending order:
\(130^\circ\text{F} > 80^\circ\text{F} > 35^\circ\text{F} > 0^\circ\text{F} > -15^\circ\text{F} > -60^\circ\text{F}\).
Examples
Understanding how to compare numbers and temperatures is essential in daily life. For example, when comparing prices, reading weather reports, or checking financial statements, converting everything to a common format (like decimals) makes it easy to see which value is larger or smaller. This skill helps in budgeting, planning for weather, and making informed decisions based on numerical data.