The range of possible values of the measurement is:
[45.97cm, 48.03cm]
Here we have the measurement:
measurement 47 cm ± 2.2%
The 2.2 percent of 47cm is:
47cm*( 2.2%/100%) = 47cm*(0.022) = 1.034 cm
Then the minimum of the measurement is:
47cm - 1.034cm = 45.97cm
The maximum of the measurement is:
47cm + 1.034cm = 48.03cm
we conclude that the correct option is the second one:
[45.97cm, 48.03cm]
If you want to learn more about ranges:
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