What is the value of the expression \frac{0.00048 \times 0.025}{0.0016} expressed in stand… — JAMB UTME

What is the value of the expression $\frac{0.00048 \times 0.025}{0.0016}$ expressed in standard form?

7.5 \times 10^{-3}

The expression evaluates step-by-step to

0.75 \times 10^{-2}

, which when written in standard form

A \times 10^n

(where

1 \le A < 10

) gives

7.5 \times 10^{-3}

Convert each decimal in the expression to standard form (powers of 10).

0.00048 = 4.8 \times 10^{-4}

0.025 = 2.5 \times 10^{-2}

, and

0.0016 = 1.6 \times 10^{-3}

Converting decimals into standard form simplifies multiplication and division using laws of indices.

Simplify the numerator.

(4.8 \times 10^{-4}) \times (2.5 \times 10^{-2}) = (4.8 \times 2.5) \times 10^{-4 + (-2)} = 12 \times 10^{-6} = 1.2 \times 10^{-5}

Multiply the numerical coefficients together and add the exponents of 10.

Divide the numerator by the denominator.

\frac{1.2 \times 10^{-5}}{1.6 \times 10^{-3}} = \left(\frac{1.2}{1.6}\right) \times 10^{-5 - (-3)} = 0.75 \times 10^{-2}

Divide the coefficients and subtract the exponent of the denominator from that of the numerator.

Convert the result into standard form (

A \times 10^n

where

1 \le A < 10

0.75 \times 10^{-2} = (7.5 \times 10^{-1}) \times 10^{-2} = 7.5 \times 10^{-3}

Standard form requires the leading coefficient to be between 1 and 10.

Fractions, Decimals, and Standard Form Conversions

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