1. Complete the table for multiplication by powers of 10 and decimals: | Column A | Column B | Column C | |----------------|-----------------|-------------------| | 5 × 100 = 500 | 6.7 × 100 = 670 | 0.39 × 100 = 39 | | 5 × 10 = 50 | 6.7 × 10 = 67 | 0.39 × 10 = 3.9 | | 5 × 1 = 5 | 6.7 × 1 = 6.7 | 0.39 × 1 = 0.39 | | 5 × 0.1 = 0.5 | 6.7 × 0.1 = 0.67| 0.39 × 0.1 = 0.039| | 5 × 0.01 = 0.05| 6.7 × 0.01 =0.067|0.39 × 0.01=0.0039 | | 5 × 0.001=0.005| 6.7 × 0.001=0.0067|0.39 × 0.001=0.00039| **Pattern description:** Multiplying by 10, 100, 1000 shifts the decimal point to the right by 1, 2, or 3 places respectively. Multiplying by 0.1, 0.01, 0.001 shifts the decimal point to the left by 1, 2, or 3 places respectively. 2. Complete the table for scientific notation: | Exponent form | Expanded form | Standard notation | |--------------------|--------------------------------|-------------------| | 2.01 × 10³ | 2.01 × 10 × 10 × 10 | 2010 | | 41.59 × 10⁵ | 41.59 × 10 × 10 × 10 × 10 × 10| 4159000 | | 3.06 × 10⁴ | 3.06 × 10 × 10 × 10 × 10 | 30600 | | 45 × 10⁻² | 45 × 0.01 | 0.45 | | 1.6 × 10⁻¹ | 1.6 × 0.1 | 0.16 | | 76.5 × 10⁻³ | 76.5 × 0.001 | 0.0765 | **Explanation:** Multiplying by $10^n$ means moving the decimal point $n$ places to the right if $n$ is positive, or to the left if $n$ is negative. Final answers are filled in the tables above.