One measurement that will require the use of irrational numbers is the diagonal of the cube.
The diagonal of a cube can be found by using the Pythagorean Theorem. Considering the cube's edge length is "a", the diagonal would be the length of the hypotenuse of a right-angled triangle with two side lengths equal to "a".
Using the Pythagorean Theorem, we have:
diagonal^2 = a^2 + a^2
diagonal^2 = 2a^2
To solve for the diagonal, we need to take the square root of both sides:
diagonal = √(2a^2)
Since the edge length "a" is given as a rational number, the square root of 2 (√2) will introduce an irrational number. Thus, the measurement of the diagonal of a cube will require the use of irrational numbers.
A cube has an edge length, a
, that is a rational number of centimeters. Identify which measurement will require the use of irrational numbers.
5 answers
Which of the following numbers could be used to specify how many cups of flour should be used in a bread recipe?
Responses
square root of 3
square root of 3
−3
negative 3
2 3/4
2 and 3 fourths
47
Responses
square root of 3
square root of 3
−3
negative 3
2 3/4
2 and 3 fourths
47
The number that could be used to specify how many cups of flour should be used in a bread recipe is 2 3/4. This is a mixed number, representing 2 whole cups and 3/4 of a cup of flour. The other options, square root of 3, -3, and 47, are not appropriate measurements for specifying the amount of flour in cups.
How do you show the group of digits that repeat in a repeating decimal?
To show the group of digits that repeat in a repeating decimal, you typically use a horizontal line (or a vinculum) over the digits that repeat. This is called a repeating decimal bar.
For example, if you have the decimal 0.333333..., where the digit 3 repeats infinitely, you would write it as 0.3 with a repeating decimal bar over the digit 3:
0.3
Similarly, for the decimal 0.272727..., where the digits 27 repeat infinitely, you would write it as 0.2 with a repeating decimal bar over the digits 27:
0.2
The repeating decimal bar helps to show which group of digits repeats indefinitely in the decimal representation.
For example, if you have the decimal 0.333333..., where the digit 3 repeats infinitely, you would write it as 0.3 with a repeating decimal bar over the digit 3:
0.3
Similarly, for the decimal 0.272727..., where the digits 27 repeat infinitely, you would write it as 0.2 with a repeating decimal bar over the digits 27:
0.2
The repeating decimal bar helps to show which group of digits repeats indefinitely in the decimal representation.
1 answer