<p>Math 123 Fall 2009</p><p>Decimals</p><p>1. How are decimals related to integers? What are the similarities between the two? Think about place value: how are different place values named?</p><p>2. How are decimals related to fractions? Can every decimal be written as a fraction?</p><p>3. How can you represent decimals using base ten blocks? For example, try 0.24, 4.32, 0.127. Is there more than one way to represent the numbers? </p><p>4. Demonstrate 0.463 + 0.507 with base 10 blocks. How is addition with blocks different for integers than for decimals? </p><p>5. Demonstrate 0.802 – 0.568 with base 10 blocks.</p><p>6. Show why 0.1 x 0.1 = 0.01 with base 10 blocks.</p><p>7. Using the previous question, give a visual representation for 1.4 x 0.3</p><p>8. Use blocks to determine which decimal number in each pair is larger: 0.5 0.28 8.3 8.14 0.07 0.068</p><p>9. In which of the following numbers is writing 0 necessary, and in which is it optional:</p><p>2.08; 0.56; 0.507; 20.6; 3.60?</p><p>10. Interpret the following problems. What is the decimal in question? What do you think would be some common incorrect responses to these problems?</p><p>1) 38 hundredths 2) 123 ten-thousandths 3) 13 tenths and 76 thousandths </p><p>11. Which decimal number is larger?</p><p>1) 52 hundredths or 731 thousandths 2) 135.7 tenths or 1.74 tens</p><p>1 12. Find a decimal between:</p><p>1) 0.5 and 0.6; 2) -1.2 and –1.15.</p><p>13. Round:</p><p>1) 3.876 to the nearest tenth 2) 1.0099 to the nearest tenth 3) 0.04534 to the nearest thousandth</p><p>14. A child is asked to add 0.25 + 0.06 using blocks and to write down his answer. He uses rods for tenths and cubes for hundredths. For 0.25 he puts down two tenth rods and 5 hundredth cubes. For 0.06 he puts down 6 hundredth cubes. Combining these together he says, “it is two tenths and 11 hundredths”, and writes down 0.211. What would you say to this child?</p><p>15. Explain the algorithm for multiplying decimals. How do you know where to put the decimal point?</p><p>16. When we divide decimals, for example, 3.4/1.5, we move the decimal point over to the right, so 3.4/1.5 = 34/15. Why can we do this?</p><p>17. The distance on a map from point A to point B along the interstate is 1.5 cm. Points C, D, and E lie, in that order, along the same interstate, but do not lie between the points A and B. The distance from B to C is one and a half times the distance from A to B. The distance from C to D is three times the distance from A to B. The distance form D to E is 1.7 cm less than twice the distance from A to D. Find the map distance, in centimeters, from A to E. On this map, 1 cm represents 38.5 km. What is the actual distance from A to E?</p><p>2</p>