Question

A sheet of plastic shrink wrap has a thickness of 0.00015 mm0.00015 \mathrm{~mm}. The sheet is 1.2 m1.2 \mathrm{~m} by 79 m79 \mathrm{~m}. Determine the volume of the sheet. Write your answer using scientific notation.

Solution

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The volume to be used is V=lwtV=lwt

From the given,

l=79l=79 m

w=1.2w=1.2 m

t=0.00015 mm=1.5×104 mm×1 m103 mm=1.5×107 mt=0.00015\text{ mm}=1.5\times10^{-4}\cancel{\text{ mm}}\times\dfrac{1\text{ m}}{10^3\cancel{\text{ mm}}}=1.5\times10^{-7}\text{ m}

So, the volume is:

V=(79)(1.2)(1.5×107)V=(79)(1.2)( 1.5\times10^{-7})

V=142.2×107 m3V=142.2\times10^{-7}\text{ m}^3

Round to 2 significant digits and convert to scientific notation:

V1.4×105 m3\color{#c34632}{V\approx1.4\times10^{-5}\text{ m}^3}

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