1. Round 10.451 to the nearest tenth.
2. John is taking a history class in which his grade for the semester is calculated by averaging his grades on five tests given throughout the class and rounding down. So far, his grades on the tests are 88, 80, 89, and 95. What is the lowest grade John can get on the last test to finish the semester with a 90 average?
3. Round 25,273.2 to the nearest thousand.
4. The median of a list of seven consecutive odd numbers is 19. What is the largest number in the list?
5. The average of six numbers is 26. After the largest number is removed, the average of the remaining numbers drops to 20. What was the value of the number that was removed?
6. In one week, Jane spends a total of $45.50 on lunch. On average, how much does she spend per day?
A. $6.50 per day
B. $6.90 per day
C. $6.95 per day
D. $7.14 per day
E. $7.20 per day
7. Rounding a number to the nearest hundredth gives 5.79. What is the smallest value that the original number could have been?
8. Calculate the median of the list of numbers.
9, 5, 23, 7, 11, 5
9. Carlos spent $420 in January, $420 in February, $500 in March, and $380 in April. On average, how much did he spend per month in this four-month period?
A. $430 per month
B. $450 per month
C. $465 per month
D. $470 per month
E. $500 per month
10. Round 6,578.49 to the nearest whole number.
1. D. When rounding, consider the digit to the right of the place value to which the number will be rounded. The tenths place is the first digit after the decimal, and the digit to its right in the hundredths place Since the digit in the hundredths place is a 5, the number in the tenths place rounds up from 4 to 5; thus, 10.451 rounded to the nearest tenth is 10.5. In other words, 10.451 is closer to 10.5 than it is to 10.4.
2. C. To find the average of five grades, add the five grades and then divide the sum by five.
John wants to his test scores to average to 90. If x represents his grade on the last test, the sum of his test scores is 88 + 80 + 89 + 95 + x. Substitute these values into the equation for the average and solve for x.
Therefore, John needs to get a 98 on the last test to finish with a 90 average for the semester.
3. B. The thousands place is the digit to the left of the comma. When rounding, consider the digit to the right of the place value to which the number will be rounded. The digit in the hundreds place is 2, which is less than five; therefore, the number will be rounded down rather than up. So, 25,273.2 rounds to 25,000. In other words, 25,273.2 is closer to 25,000 than to 26,000
4. A. The median of a list of numbers is the middle number after the numbers are listed increasing order. In a set of seven numbers listed from least to greatest, the median is the fourth number in the list. Since the median of this set of consecutive off integers is 19, it is the fourth number. Determine the three consecutive odd integers which follow 19.
13, 15, 17, 19, 21, 23, 25
The largest number in the list is 25.
5. E. To find the value of the number that was removed, first find the sum of all six numbers. Then, find the sum of the five remaining numbers after the largest number is removed. Finally, subtract the smaller sum from the larger to determine the value of the number removed from the set of six..
Given that the average of all six numbers is 26, find their sum.
Sum = 156
Find the sum of the five numbers which remain after the largest number is removed.
Sum = 100
Finally, subtract these two sums to find the value of the removed number. Since 156 – 100 = 56, the number that was removed was 56.
6. A. To calculate the average, divide the total, $45.50, by the number of days in a week, 7.
Therefore, Jane spent an average of $6.50 per day on lunch.
7. C. In order for a number to round to 5.79, that number would have to be greater than or equal to 5.785 but less than 5.795
Therefore, the smallest value that the original number could have been is 5.785.
8. D. The median of a list of numbers is the middle number after the numbers are listed in increasing order. So the first step is to list the numbers in increasing order.
5, 5, 7, 9, 11, 23
Since there are six numbers, the list does not have a middle number. When this occurs, the median is defined as the average of the two middle numbers. To find the median of this set of numbers, calculate the average of 7 and 9, the middle two numbers.
Therefore, the median is 8.
9. A. To find the average, calculate the sum of the four numbers and divide by four.
Sum = 420 + 420 + 500 + 380 + = 1720
Therefore, Carlos spent $430 per month on average.
10. B. When rounding, consider the digit to the right of the place to which the number will be rounded. Since this number will be rounded to the nearest whole number, look at the digit in the tenths place to determine whether the number will be rounded to 6,578 or to 6,579. The number in the tenths place is less than five, so 6,578.49 rounds to 6,578.