Discussion
If p = (12·34 × \(10^{10}\)) - (5·67 × \(10^{9}\)), then p is expressed in standard form as :
Answer: A
In standard form p is \(1{\cdot}1773 \times 10^{11}\).
Write both terms with the same power of ten before subtracting:
\[ \begin{aligned} p &= 123{\cdot}4 \times 10^{9} - 5{\cdot}67 \times 10^{9} \\ &= 117{\cdot}73 \times 10^{9} \\ &= 1{\cdot}1773 \times 10^{11} \end{aligned} \]
\(1{\cdot}1773 \times 10^{10}\) moves the decimal point one place too few. \(1{\cdot}773 \times 10^{11}\) and \(1{\cdot}773 \times 10^{10}\) drop a digit, as happens when the two numbers are subtracted without first matching their powers of ten.
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