Exercises

1. 1. Multiply.
      1. \(0.8 \times 5\)
      2. \(2.4 \times 2.5\)
      3. \(0.5 \times 2.1\)
      4. \(1.1 \times 0.009\)
   2. Explain for each of the above products how you can check that your answers are reasonable. For example, in part i), the product \(0.8 \times 5\) should be less than \(5\) because \(0.8\) is less than \(1\), but should also be greater than \(2.5\) because \(0.8\) is greater than \(0.5\). 
2. Place a \(\lt\), \(\gt\), or \(=\) in each box to make the statement true.
   1. \(7810 \quad \boxed{\phantom\square} \quad 7.81 \times 10^2\)
   2. \(-1.32 \times 10^4 \quad \boxed{\phantom\square} \quad -3.32 \times 10^4\)
   3. \(870~000 \quad \boxed{\phantom\square} \quad 8.7 \times 10^5\)
   4. \(16~000~000~000~000 \quad \boxed{\phantom\square} \quad 6.1 \times 10^{13}\)
3. From the numbers given, find the pair with a product closest to
   \[7.9 \quad\quad 6.3 \quad\quad 3.8\]\[8.8 \quad\quad 2.8 \quad\quad 7.2\]
   1. \(10\)
   2. \(30\)
   3. \(50\)
4. 1. Suppose each of the numbers below is multiplied by \(73.9\). Which numbers would give a product less than \(73.9\) and which numbers would give a product greater than \(73.9\)?\[1.23 \qquad 0.4 \qquad 1.02 \qquad 1.17 \qquad 0.0013 \qquad 0.29\]
   2. Which product would be the greatest? Which product would be the least?
5. Brextyn placed four textbooks, each with a mass of \(0.9\) kg, on a digital scale. What was the total mass displayed on the scale?
6. Human bones make up \(18\%\) of our body mass. Jason's mass is \(59.2\) kg.  What is the mass of his bones?
7. A bottle holds \(0.7\) litres of juice. How many litres will \(2 \dfrac{1}{2}\) bottles hold?
8. The product of two decimal numbers is \(8\).
   1. What might the two numbers be?
   2. Find three additional pairs of decimal numbers that have a product of \(0.8\).
9. Omar said that to multiply \(1.7 \times 1.7\), you can multiply \(1 \times 1\) and \(0.7 \times 0.7\) and the answer is \(1.49\). Is Omar's strategy correct? Explain.
10. Consider the following sequence of numbers.\[0.1, ~0.01, ~0.001,~ 0.0001, \ldots\] In this sequence, each term is \(0.1\) times the previous term. Explain the pattern that is generating each of the following sequences?
    1. \(0.1, ~-0.01,~ 0.001,~ -0.0001, \ldots\)
    2. \(-0.5, ~-1.5, ~-4.5, ~-13.5, \ldots\)
    3. \(-0.2,~ 0.4,~ -0.8,~ 1.6, \ldots\)