Final answer:
The number ten can create new numbers through integer powers (10^3 = 1,000), in metric system conversions (1 km = 10^3 meters), and through reciprocals that multiply to 10 (such as 2 and 5). The powers-of-ten notation reflects our base-10 counting system, which developed from the practice of counting with fingers.
Step-by-step explanation:
The number ten can be incorporated into creating new numbers in various ways. Here are three examples:
- By using integer powers, for instance, 103 is 10 multiplied by itself three times, which equals 1,000.
- In the metric system, powers of 10 are used for conversions, such as 1 kilometer being 103 meters or 1,000 meters.
- For quick mental math, understanding reciprocals that multiply to 10 can be helpful, such as 2 and 5 because 2 × 5 equals 10.
The number ten's significance is rooted in the powers-of-ten notation, which is a fundamental part of our counting system, reflecting each place's value being ten times greater than the place to its right. This system originated from humans using their ten fingers to count.