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Evaluate 0.12 / (4.56x3.6) and express

Mathematics

ScanSolve AI Answer

Answer

1.368×1021.368 \times 10^2

Step-by-step solution

8 steps

The problem asks to evaluate 4.56×3.60.12\frac{4.56 \times 3.6}{0.12} without a calculator and express the answer in standard form.

  1. Convert the decimals to fractions to simplify the calculation.

    4.56=4561004.56 = \frac{456}{100} 3.6=36103.6 = \frac{36}{10} 0.12=121000.12 = \frac{12}{100}
  2. Substitute these fractions into the expression.

    456100×361012100\frac{\frac{456}{100} \times \frac{36}{10}}{\frac{12}{100}}
  3. Simplify the numerator.

    456×36100×10=456×361000\frac{456 \times 36}{100 \times 10} = \frac{456 \times 36}{1000}
  4. Rewrite the entire expression and perform the division by multiplying by the reciprocal of the denominator.

    456×361000÷12100=456×361000×10012\frac{456 \times 36}{1000} \div \frac{12}{100} = \frac{456 \times 36}{1000} \times \frac{100}{12}
  5. Simplify by canceling common factors.

    Notice that 36÷12=336 \div 12 = 3.
    Also, 1001000=110\frac{100}{1000} = \frac{1}{10}.

    456×310\frac{456 \times 3}{10}
  6. Perform the multiplication in the numerator.

    456×3=(400×3)+(50×3)+(6×3)=1200+150+18=1368456 \times 3 = (400 \times 3) + (50 \times 3) + (6 \times 3) = 1200 + 150 + 18 = 1368
  7. Divide the result by 10.

    136810=136.8\frac{1368}{10} = 136.8
  8. Express the answer in standard form (a×10na \times 10^n, where 1≤∣a∣<101 \le |a| < 10).

    To get 136.8 into standard form, move the decimal point two places to the left.

    136.8=1.368×102136.8 = 1.368 \times 10^2

    The answer is 1.368×1021.368 \times 10^2.

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