Activities

1. Define rounding
   
   
2. Which number is correct when rounding 6.8 to the ones place?   
   
   1. 6.80
   2. 6
   3. 7
      
      
3. Round .492 to the hundredths place.
   
   
4. When 1.09 is rounded to the tenths place, the answer is 1.1     True or false?
   
   
5. List the process for rounding a number to the hundredths place.

6. Complete the chart by indicating what place value each number was rounded to.

7. Identify the number that was rounded to the tenths place.
   1. 42.094
   2. 42.09
   3. 42.1
   4. 40.89
      
      
8. Camron was going to the store to buy a soda that cost $1.14.  He rounded to the tenths place and asked his mother for that amount.  Explain why rounding to the tenths place in this situation will not work for Cameron.
   
   
9. The number 19.32 has been rounded to the hundredths place.  The number 19.32x was the original.  List the digits that are possible values of x before 19.32 was rounded.
   
   
10. Round 23.758 to the hundredths place and then round that number to the ones place.
    
    
11. Explain why it is necessary for a number to have digits to the thousandths place when rounding to the hundredths place.
    
    
12. The first number has not been rounded.   The second number is the first number that has been rounded.  Identify the place each pair has been rounded to (ones, tenths, hundredths, thousandths).

13. Round 26.427 to any place other than tenths.  What place did you round to?
    
    
14. How do you know the number 72.009 was not rounded to the ones place?
    
    
15. Explain how you know 37.129 was not rounded to the hundredths place.

16. State the rule or steps for rounding decimals and explain why it would not be appropriate for a digit of 3 to be the value for deciding whether to round a number up or down.
    
    
17. Describe a real world situation where it would be appropriate to round 23.49 to 24.  Justify your reasoning.
    
    
18. Describe a real world situation where it would not be appropriate to round 16.392 to 16. Justify your reasoning.
    
    
19. If x is greater than or equal to 5, what digit can be substituted for y so that .y4x will be a whole number when rounded to the hundredths place and then to the tenths place?
    
    
20. If x is less than 3, is it possible to round 4.6yx to the hundredths place and get 4.7?  If yes, what digits are possible for y?  Justify your answer.  If no, explain why it is not possible.
    
    
21. It is not possible for the number 19.0xy to be rounded to 20 when rounding to the tenths or hundredths place.  True or false?  Justify your answer and provide the digits that would be substituted for x and y to prove your answer.
    
    
22. Is there a number, that when rounded to the ones, tenths, hundredths and thousandths, has the same answer for each rounding?  If yes, what is it?  If no, explain why not.
    
    
23. What value of x and y will make the number 6.xy4 have the same solution when rounded to each of the following place values?  Tenths and hundredths.  Explain your reasoning.
    
    
24. The number 16.895 is being rounded to the tenths place.  Describe a real world situation that would justify why this number should not be rounded to tenths place.  Explain your thinking.
    
    
25. How many numbers are there that when rounded to the tenths or hundredths place, the solution is the same, given the conditions below?  Explain your reasoning.

• Number is less than one
• Number has a 4 in the thousandths place
• Number has digits in the tenths, hundredths and thousandths places

Answer Key/Rubric

1. Rounding a number is when you take a number and "bump it up" or "bump it down" to a nearby and "cleaner" number. A number can be rounded to any place value you want.
   
   
2. c
   
   
3. .49
   
   
4. True
   
   
5. Locate the digit in the thousandths place.  If it is greater than 5, increase the number in the hundredths place by one digit and remove the thousandths place digit.  If it is less than 5, just remove the thousandths place digit.

6. See chart
   
   
7. c
   
   
8. Explanations will vary – need to include a reference to the fact that when rounding this number to the tenths place it will be less money than he needs
   
   
9. 1, 2, 3, 4,
   
   
10. 23.76  and then 24
    
    
11. Explanations will vary; number needs to go beyond the place value you need to round to or there is no way to determine how to round the number
    
    
12. 

Hundredths                 ones                 tenths                             tenths                       thousandths 

13. Answers will vary 26 – ones, 26.43 – hundredths
    
    
14. Answers will vary – need something about there are still digits in the tenths, hundredths and thousandths places
    
    
15. Answers will vary – need something about there are digits still in the thousandths place.

16. Answers will vary.  Example using rounding to the hundredths place:  Locate the digit in the thousandths place.  If it is greater than 5, increase the number in the hundredths place by one digit and remove the thousandths place digit.  If it is less than 5, just remove the thousandths place digit.  Explanation needs something about 5 being half way or in the middle between 0 and 9
    
    
17. Answers will vary – example would be a money situation – you would have enough money to pay at the store if you rounded up (not worrying about tax)
    
    
18. Answers will vary – example would be a situation where a precise measurement is needed, such as cutting a piece for a part of a machine because the machine would not run if the part was not precise
    
    
19. 9, because in order for it to be bumped up to a whole number the y must be 9 so it would go up one and become 1.0; otherwise it will still be a decimal value
    
    
20. No x must be greater than or equal to 5.  Answers will vary – student must indicate that any digit greater than 5 will cause the y digit to be rounded up which is the only way it is possible to get 4.7 when rounding to the hundredths place (y must 9 in order for this to be possible).
    
    
21. True, x and y can be any digit – the zero in the tenths place prevents the number from being rounded to 20 – when rounding to the tenths place the hundredths place must be greater than 5 and the tenths place must be 9 – when rounding to the hundredths place the tenths and the hundredths places need to be a 9 with the thousandths place greater than 5.
    
    
22. Yes, possible answers are x.0001; x.0002; x.0003; x.0004; x.9995; x.9996; x.9997; x.9998; x.9999      where x can be any number.
    
    
23. x = any digit and y = 0 when rounded to both places the answer will be the same. 
    
    
24. Answers will vary.  Example:  when referring to objects that do not have fractional parts such as people.
    
    
25. 10 numbers.  Explanations  should indicate that in order for the solution to be the same the hundredths place must be a 0 so that when you round to either the tenths or the hundredths place the number will not change ( .9 is the same as .90) ; for example  .xy4  will give 10 solutions when x is any digit 0 - 9 and y = 0