Evaluate the numerical expression \frac{0.00054 \times 0.002}{0.00036} and state the final… — JAMB UTME

Evaluate the numerical expression $\frac{0.00054 \times 0.002}{0.00036}$ and state the final result as a decimal.

Cevap: 0.003

The correct value as a decimal is 0.003.

Converting all terms to scientific notation yields

\frac{(5.4 \times 10^{-4}) \times (2 \times 10^{-3})}{3.6 \times 10^{-4}} = \frac{10.8 \times 10^{-7}}{3.6 \times 10^{-4}} = 3 \times 10^{-3} = 0.003

Convert each decimal in the expression to scientific notation (standard form)

0.00054 = 5.4 \times 10^{-4}

0.002 = 2 \times 10^{-3}

0.00036 = 3.6 \times 10^{-4}

Converting decimals with leading zeros to powers of 10 prevents errors in decimal point alignment during multiplication and division.

Simplify the numerator by multiplying coefficients and adding exponents

(5.4 \times 10^{-4}) \times (2 \times 10^{-3}) = 10.8 \times 10^{-7}

According to the laws of indices,

10^a \times 10^b = 10^{a+b}

, so

-4 + (-3) = -7

Divide the simplified numerator by the denominator

\frac{10.8 \times 10^{-7}}{3.6 \times 10^{-4}} = \left(\frac{10.8}{3.6}\right) \times 10^{-7 - (-4)} = 3.0 \times 10^{-3}

Dividing the coefficients gives

10.8 \div 3.6 = 3

, and subtracting the exponents gives

-7 - (-4) = -3

Express the result in standard decimal form

3.0 \times 10^{-3} = 0.003

Shifting the decimal point 3 positions to the left converts

10^{-3}

to standard decimal representation.

Simplifying Decimal Expressions using Standard Form and Laws of Indices

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