This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The problem asks to evaluate (4.56 × 3.6)/(0.12) without a calculator and express the answer in standard form. Step 1: Convert the decimals to fractions to simplify the calculation. 4.56 = (456)/(100) 3.6 = (36)/(10) 0.12 = (12)/(100) Step 2: Substitute these fractions into the expression. (456)/(100) × (36)/(10)(12)/(100) Step 3: Simplify the numerator. (456 × 36)/(100 × 10) = (456 × 36)/(1000) Step 4: Rewrite the entire expression and perform the division by multiplying by the reciprocal of the denominator. (456 × 36)/(1000) ÷ (12)/(100) = (456 × 36)/(1000) × (100)/(12) Step 5: Simplify by canceling common factors. Notice that 36 ÷ 12 = 3. Also, (100)/(1000) = (1)/(10). (456 × 3)/(10) Step 6: Perform the multiplication in the numerator. 456 × 3 = (400 × 3) + (50 × 3) + (6 × 3) = 1200 + 150 + 18 = 1368 Step 7: Divide the result by 10. (1368)/(10) = 136.8 Step 8: Express the answer in standard form (a × 10^n, where 1 |a| < 10). To get 136.8 into standard form, move the decimal point two places to the left. 136.8 = 1.368 × 10^2 The answer is 1.368 × 10^2. What's next?