1. **Problem:** Write the missing word and show how to shift the decimal when multiplying or dividing by powers of 10. 2. **Rule:** Multiplying by 10, 100, 1000, etc., shifts the decimal point to the right by as many zeros as in the multiplier. Dividing by 10, 100, 1000, etc., shifts the decimal point to the left by as many zeros as in the divisor. 3. **Examples:** - a) $3.6 \times 10 = 36$ (decimal moves 1 place right) - b) $7.5 \times 1000 = 7500$ (decimal moves 3 places right) - c) $0.041 \times 100 = 4.1$ (decimal moves 2 places right) - d) $200.75 \times 100 = 20075$ (decimal moves 2 places right) - e) $0.409 \times 100000 = 40900$ (decimal moves 5 places right) - f) $23083 \div 10000 = 2.3083$ (decimal moves 4 places left) 4. **Number line explanation:** Shifting decimal right means multiplying by 10, 100, etc., shifting left means dividing. 5. **Second set:** - a) $4.24 \times 10 = 42.4$ - b) $40.003 \div 100 = 0.40003$ - c) $0.001 \times 1000 = 1$ - d) $60.07 \times 1000 = 60070$ - e) $134 \div 10000 = 0.0134$ 6. **Third set:** - a) $3.7 \times 10 = 37$ - b) $4.03 \times 100 = 403$ - c) $0.056 \times 10 = 0.56$ - d) $9.6 \times 100 = 960$ - e) $0.9 \times 1000 = 900$ - f) $23000 \div 10000 = 2.3$ 7. **Fourth set:** Express numbers as sums of place values: - a) $3.54 = 3$ tens $+ 5$ ones $+ 4$ tenths - b) $2.19 = 2$ ones $+ 1$ tenth $+ 9$ hundredths 8. **Fifth set:** Multiply and regroup if needed: - a) $2 \times 6.2 = 12.4$ - b) $0.4 \times 5 = 2$ - c) $7.3 \times 8 = 58.4$ - d) $6.9 \times 3 = 20.7$ 9. **Sixth set:** Find products: - a) $8 \times 4.8 = 38.4$ - b) $7 \times 0.5 = 3.5$ - c) $8 \times 5.2 = 41.6$ - d) $2 \times 2.5 = 5$ - e) $3 \times 36.0 = 108$ - f) $0 \times 4.7 = 0$ - g) $6 \times 2.8 = 16.8$ - h) $6 \times 0.62 = 3.72$ - i) $4 \times 5.80 = 23.2$ - j) $6 \times 4.12 = 24.72$ - k) $5 \times 28.75 = 143.75$