Interpreting Decimals Numbers

Math 123 Fall 2009

Decimals

1. How are decimals related to integers? What are the similarities between the two? Think about place value: how are different place values named?

2. How are decimals related to fractions? Can every decimal be written as a fraction?

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?

4. Demonstrate 0.463 + 0.507 with base 10 blocks. How is addition with blocks different for integers than for decimals?

5. Demonstrate 0.802 – 0.568 with base 10 blocks.

6. Show why 0.1 x 0.1 = 0.01 with base 10 blocks.

7. Using the previous question, give a visual representation for 1.4 x 0.3

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

9. In which of the following numbers is writing 0 necessary, and in which is it optional:

2.08; 0.56; 0.507; 20.6; 3.60?

10. Interpret the following problems. What is the decimal in question? What do you think would be some common incorrect responses to these problems?

1) 38 hundredths 2) 123 ten-thousandths 3) 13 tenths and 76 thousandths

11. Which decimal number is larger?

1) 52 hundredths or 731 thousandths 2) 135.7 tenths or 1.74 tens

1 12. Find a decimal between:

1) 0.5 and 0.6; 2) -1.2 and –1.15.

13. Round:

1) 3.876 to the nearest tenth 2) 1.0099 to the nearest tenth 3) 0.04534 to the nearest thousandth

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?

15. Explain the algorithm for multiplying decimals. How do you know where to put the decimal point?

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?

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?