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Grade 8 · Number · Scientific Notation and Real Numbers

Map the Real Number System

Scientific notation compresses very large and very small numbers. The real number system includes rational numbers and irrational numbers such as π and √2.

The big idea

Notation reveals magnitude

In 4.6 × 10⁻⁵, the exponent shows repeated division by ten. A square root such as √20 is irrational, but nearby perfect squares locate it between 4 and 5.

Work it through

Compare 3.2 × 10⁶ and 4.9 × 10⁵

  1. 1. Compare exponents first: 10⁶ represents ten times the place value of 10⁵.
  2. 2. Rewrite if helpful: 3.2 × 10⁶ = 3,200,000.
  3. 3. Rewrite 4.9 × 10⁵ = 490,000.
  4. 4. Therefore 3.2 × 10⁶ is greater.