1.) Find a rational number between 7 and 8. Write your answer as a rational number.
2.) Find a fractional number between 2 1/16 and 4 1/9
3.) Find an irrational number between 7 and 8. Explain your answer.
4.) Find an irrational number between 2 ⅙ and 2 ½.
5.) Find a rational number between 𝝅 and √12. Show your work.
1) One rational number between 7 and 8 is 7.5, because it can be written as 15/2.
2) To find a fractional number between 2 1/16 and 4 1/9, we can take the average of the two numbers.
2 1/16 = (33/16)
4 1/9 = (37/9)
Adding them and dividing by 2:
(33/16 + 37/9) / 2 = (297/144 + 592/144) / 2 = 889/144 / 2 = 889/288
Therefore, the fractional number between 2 1/16 and 4 1/9 is 889/288.
3) An irrational number between 7 and 8 could be √7.5 because it falls between the two given numbers and cannot be expressed as a fraction or a terminating or repeating decimal.
4) To find an irrational number between 2 1/6 and 2 1/2, we can take the average of the two numbers.
2 1/6 = (13/6)
2 1/2 = (5/2)
Adding them and dividing by 2:
(13/6 + 5/2) / 2 = (13/6 + 15/6) / 2 = 28/6 / 2 = 14/6 = 7/3
Therefore, the irrational number between 2 1/6 and 2 1/2 is 7/3.
5) To find a rational number between 𝝅 and √12, we can approximate √12 as 3.464.
Since 𝝅 is approximately 3.14159, we can take the average of 𝝅 and √12.
(3.14159 + 3.464) / 2 = 6.60559 / 2 = 3.302795
Therefore, a rational number between 𝝅 and √12 is approximately 3.302795.
define - Area Formula for a square and rectangle -
define - Quantitative relationships -
define - Interpreting Irrational answers for time and money -
1.) True or false: the √ 20 is between the integers 4 and 5.
2.) If a square room has a floor with an area of 289 square feet, how long is each side of the floor?
3.) If a square cube has a volume of 729 cubic feet, how long is each side of the cube?
4.) Is the √65 closer to the integer 8 or 9?
5.) Is the fraction ⅓ a repeating or terminating decimal?
- The area formula for a square is A = s^2, where s is the length of one side of the square.
- The area formula for a rectangle is A = l x w, where l is the length and w is the width of the rectangle.
- Quantitative relationships refer to the mathematical relationships between quantities, such as ratios, proportions, and equations. It involves analyzing and interpreting numerical data to understand the relationships and patterns within the data.
- When interpreting irrational answers for time and money, it means that the answer may not be exact or precise. For example, if the calculation results in an irrational number for the duration of time or amount of money, it means that the exact value cannot be represented as a finite decimal or fraction. It is often necessary to round or approximate these irrational answers to practical or reasonable values.
1) True, because √20 is approximately 4.47, which falls between the integers 4 and 5.
2) To find the length of each side of a square room with an area of 289 square feet, you take the square root of the area.
√289 = 17
Therefore, each side of the square room is 17 feet long.
3) To find the length of each side of a cube with a volume of 729 cubic feet, you take the cube root of the volume.
∛729 = 9
Therefore, each side of the square cube is 9 feet long.
4) √65 is closer to the integer 8 because √65 ≈ 8.06, which is closer to 8 than 9.
5) ⅓ is a repeating decimal because when divided, it becomes 0.33333... with the digit 3 repeating indefinitely.