A tram company records small delays using negative indices, so that a very short delay can be written neatly as a power of 5 rather than a long decimal. Eng...
Question 1 Report
A tram company records small delays using negative indices, so that a very short delay can be written neatly as a power of 5 rather than a long decimal. Engineers use the decimal form when comparing readings across different drones.
- Write \(5^{-3}\) as a single fraction in its simplest form. (1)
- Work out the value of \(5^{-3}\) as a decimal. (2)
Answer Details
This question tests writing a negative power as a fraction, then converting that fraction to a decimal.
(a) A negative power means "take the reciprocal of the positive power":
\[ 5^{-3} = \frac{1}{5^3} = \frac{1}{125} \] [1 mark]
(b) Dividing 1 by 125 gives the decimal form:
\[ \frac{1}{125} = 0.008 \] [2 marks]
Writing a small delay as \( 5^{-3} \) is compact for engineers comparing readings symbolically, but the decimal form \( 0.008 \) is what is actually needed when comparing sizes numerically at a glance.
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