Real Numbers

Mathematics — Second Preparatory

Real numbers on the number line and their order

Every real number corresponds to exactly one point on the number line, and every point on the line represents a real number.
To locate an irrational number such as √7, we compare it with the squares of nearby integers:

2² = 4 and 3² = 9. Since 4 < 7 < 9, we have 2 < √7 < 3.
2.6² = 6.76 and 2.7² = 7.29. So √7 lies between 2.6 and 2.7, and is closer to 2.65.
To order numbers from smallest to largest, write each one as a decimal approximation and compare them.

Real Numbers · 4 / 7