Evaluate \(3.0\times 10^1 - 2.8\times 10^{-1}\)leaving the answer in standard form

  • A \(2\times 10^{-1}\)
  • B \(2\times 10^{2}\)
  • C \(2.972 \times 10^{1}\)
  • D \(2.972 \times 10^{2}\)
waec 1998mathematics

The correct answer is C. \(2.972 \times 10^{1}\)

To evaluate the expression \(3.0\times 10^1 - 2.8\times 10^{-1}\), we need to make the exponents of the powers of 10 the same.

We can do this by multiplying and dividing the second term by \(10^2\), which gives:

\(3.0\times 10^1 - 2.8\times 10^{-1} = 3.0\times 10^1 - \frac{2.8\times 10^{-1} \times 10^2}{10^2}\)

\(= 3.0\times 10^1 - \frac{2.8\times 10^1}{10^2}\)

\(= 3.0\times 10^1 - 0.028\times 10^1\)

Now, we can subtract the terms with the same exponent, which gives:

\(= (3.0 - 0.028)\times 10^1\)

\(= 2.972\times 10^1\)

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