Explain how to distinguish between a rational number and an irrational number.

Irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point

Any number in fraction form is rational number.

[Exception.- 0 is a rational number, always remember that].

SAMPLE RESPONSE: A rational number can be expressed as a whole number, a fraction, or decimal that has either terminating or repeating digits. A square root of a perfect square is rational. If it is none of these, then the number is irrational.

Step-by-step explanation:

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(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.