Which number is irrational? โ โ7.โ7 โ 2.6457โฆ never terminates or repeats. โ9 = 3 is rational, as are 0.25 and โ3/4.
Which of these is a rational number? โ โ16.โ16 = 4, a whole number, so it is rational. The others cannot be expressed as p/q.
Is 0.666โฆ (0.6ฬ) rational or irrational? โ Rational โ it is a repeating decimal.Repeating decimals are always rational. 0.666โฆ = 2/3.
Which statement best defines a rational number? โ A number that can be written as p/q where p and q are integers and q โ 0.The definition of rational is expressible as the ratio of two integers with a nonzero denominator.
The number ฯ is irrational because: โ Its decimal expansion never terminates and never repeats.Irrationality is defined by the decimal behavior: non-terminating and non-repeating.
Which of these square roots is rational? โ โ49.โ49 = 7, a whole number. The others are not perfect squares.
Between which two integers does โ30 lie? โ 5 and 6.5ยฒ = 25 < 30 < 36 = 6ยฒ, so 5 < โ30 < 6.
Which of the following is NOT a perfect square? โ 50.50 = 2 ร 25 is not a perfect square (โ50 is irrational). The others equal 5ยฒ, 10ยฒ, 12ยฒ.
Between which two consecutive integers does โ10 lie? โ 3 and 4.3ยฒ = 9 < 10 < 16 = 4ยฒ, so 3 < โ10 < 4.
Between which two consecutive integers does โ45 lie? โ 6 and 7.6ยฒ = 36 < 45 < 49 = 7ยฒ, so 6 < โ45 < 7.
Approximate โ2 to the nearest tenth. โ 1.4.1.4ยฒ = 1.96 and 1.5ยฒ = 2.25. Since 1.96 is closer to 2 than 2.25 is, โ2 โ 1.4.
Which statement about โ20 is correct? โ โ20 is between 4 and 5.4ยฒ = 16 < 20 < 25 = 5ยฒ, so 4 < โ20 < 5.
What is the best first step to approximate โ75? โ Find the perfect squares on each side: 8ยฒ = 64 and 9ยฒ = 81.The squeezing method always starts by identifying the consecutive perfect squares that bound the radicand.
โ3 is approximately: โ 1.73.1.73ยฒ = 2.9929 โ 3. The correct approximation of โ3 is about 1.732.
What does "squeezing" mean when approximating โn? โ Finding perfect squares that bound n, then narrowing the interval.The squeezing method locates two values whose squares straddle n, then iteratively narrows the interval.
Approximate โ99 to the nearest integer. โ 10.10ยฒ = 100, so โ99 is just under 10. โ81 = 9 and โ100 = 10, and since 99 is much closer to 100, the nearest integer is 10.
Why can we not express โ5 as a finite decimal? โ โ5 is irrational โ its decimal expansion never terminates or repeats.Irrational numbers, by definition, cannot be expressed as terminating or repeating decimals.
Which property is shown by: 3 + 7 = 7 + 3? โ Commutative property of addition.Swapping the order of addition illustrates the commutative property: a + b = b + a.
What is the additive identity for real numbers? โ 0.a + 0 = a for any real number a. Zero is the additive identity.
What is the multiplicative identity for real numbers? โ 1.a ร 1 = a for any real a. One is the multiplicative identity.
Which property is shown by: (2 + 3) + 4 = 2 + (3 + 4)? โ Associative property of addition.Regrouping without changing order illustrates the associative property: (a + b) + c = a + (b + c).
The additive inverse of โ5 is: โ 5.The additive inverse of a is โa. The additive inverse of โ5 is โ(โ5) = 5, since โ5 + 5 = 0.
The multiplicative inverse of 3/4 is: โ 4/3.The multiplicative inverse (reciprocal) of 3/4 is 4/3, since (3/4)(4/3) = 1.
Which expression demonstrates the distributive property? โ 4(x โ 2) = 4x โ 8.Distributing 4 over (x โ 2) gives 4x โ 8. The others show commutative, associative, and identity properties.
Which of these is an example of the commutative property of multiplication? โ 5 ร โ3 = โ3 ร 5.Swapping the order of factors shows commutativity: a ร b = b ร a.
If (a + b) + c = a + (b + c), which property is this? โ Associative property of addition.Regrouping addends without reordering them is the associative property.