1. Bell Work Which number is twice as much as the square root of ten
Bell Work Which number is twice as much as the square root of ten? √20 or √40

2. Answer: √40

3. Lesson 17: Rounding and Estimating

4. We often use rounding and estimating for situations in which an exact or nearly exact number is not necessary. Round*: to find a nearby number that ends with one or more zeros.

5. The mathematical procedure for rounding involves place value
The mathematical procedure for rounding involves place value. We round a number to a certain place value by inspecting the digit that follows that place and deciding whether to round up or down.

6. Example: Round 1,481,362 to the nearest hundred thousand.

7. Answer: 1,481,362 The number is between 1,400,000 and 1,500,000
Answer: 1,481,362 The number is between 1,400,000 and 1,500,000. The digit in the ten- thousands place is 8, so we round up to 1,500,000.

8. We round decimal numbers by finding a decimal number with fewer decimal places. The procedure is similar to the one used for whole numbers except that we do not use trailing zeros.

9. Example: Round 3.14159 to two decimal places.

10. Answer: “Two decimal places” means two places to the right of the decimal point. The digit in the thousandths place is 1 which is less than 5, so we round down to 3.14.

11. To round a mixed number to the nearest whole number, we decide if the fraction is more than or less than ½. If the numerator is less than half the denominator, then the fraction is less than ½, and we round down. If the numerator is half or greater than half of the denominator, we round up.

12. Example: Round each number to the nearest whole number. 13 5/12 13.512

13. Answer: 13 5/12 = the fraction 5/12 is less than ½ because 5 is less than half of 12. We round down to = the digit in the first decimal place is 5, so we round up to 14.

14. Estimate*: to determine an approximate answer.

15. Estimating calculations helps us decide if an answer is reasonable
Estimating calculations helps us decide if an answer is reasonable. For example, suppose we are calculating the cost of 48 square yards of carpeting priced at $28.95 per square yard. We could round the quantity to 50 square yards and price to $30 per square yard. Multiplying these numbers mentally we get $1500. If the calculated product is very different, then the results are not reasonable and we will review our calculations.

16. Example: Kaitlyn wants to tile the floor of a kitchen that is 12 feet long and 8 feet wide. The installed tile is $7.89 per square foot. Kaitlyn calculates that the cost to tile the floor is $ Are her calculations reasonable?

17. Answer: The cost is based on the number of square feet
Answer: The cost is based on the number of square feet. The are of the kitchen is 8ft x 12ft or 96 square feet. We can estimate the cost of tiling the floor by multiplying 100 square feet by $8 per square foot. A reasonable estimate of the cost is $800, which is very different from Kaitlyn’s calculation. Since her calculation is not reasonable, she should check her calculations.

18. Example: Jake is paid $11. 85 per hour
Example: Jake is paid $11.85 per hour. About how much money does he earn in a year (52 weeks) if he works 40 hours per week?

19. Answer: Total pay ≈ $12 x 40 x 50 ≈ $12 x 2000 ≈ $24,000 per year

20. Practice: In 2000 the population of Dallas was 1,188,580
Practice: In 2000 the population of Dallas was 1,188,580. Round that number to the nearest hundred thousand.

21. Answer: 1,200,000

22. Practice: Estimate the height of the ceiling in your classroom in feet.

23. Answer: Measure to see if estimation was correct.

24. HW: Lesson 17 #1-30 Due Tomorrow