Question

evaluate: (0.3)(0.3)-(0.2)(0.2)

Answer 1

(0.3)(0.3) - (0.2)(0.2)

= (0.3)^2 - (0.2)^2

= 0.09 - 0.04

= 0.05

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Answer 2

Answer:

(0.3)(0.3)-(0.2)(0.2) = 0.05

Step-by-step explanation:

• Step - 1: Evaluation of (0.3)(0.3)

        0.3 can be written as, 0.3 = $\frac{3}{10}$

        (0.3)(0.3) means 0.3 × 0.3

                                   = $\frac{3}{10}$ × $\frac{3}{10}$   [ as  0.3 = $\frac{3}{10}$ ]

                                   = $\frac{9}{100}$ = 0.09

• Step - 2: Evaluation of (0.2)(0.2)

        0.2 can be written as, 0.2 = $\frac{2}{10}$

        (0.2)(0.2) means 0.2 × 0.2

                                    = $\frac{2}{10}$  × $\frac{2}{10}$     [ as  0.2 = $\frac{2}{10}$ ]

                                   = $\frac{4}{100}$ = 0.04

• Step - 3: Subtraction:

        (0.3)(0.3)-(0.2)(0.2) = (0.3 × 0.3) - (0.2 × 0.2)

                                        = 0.09 - 0.04

                                        = 0.05

    ∴The final answer will be 0.05

[Alternative method:  (0.3)(0.3) = (0.3)² and (0.2)(0.2) = (0.2)²

                                     As (a² - b²) = (a + b)(a - b)]

                                     (0.3)(0.3)-(0.2)(0.2) = (0.3)² - (0.2)²

                                                                     = (0.3 + 0.2)(0.3 - 0.2)

                                                                     = 0.5 × 0.1

                                                                     = 0.05]