Express the following sum with the correct number of significant figures:\(1.80\;{\rm{m}} + 142.5\;{\rm{cm}} + 5.34 \times {10^5}\;{\rm{\mu m}}\)

A significant figure can be defined as the number of digits that are necessary to determine or identify the value of a particular quantity.

Given data:

The first value is 1.80 m.

The second value is 142.5 cm.

The third value is\(5.34 \times {10^5}\;{\rm{\mu m}}\).

Unit conversion:

Now, converting the unit,

\(\begin{aligned}{c}142.5\;{\rm{cm}} = 142.5 \times {10^{ - 2}}\;{\rm{m}}\\ = 1.{\rm{425}}\;{\rm{m}}\end{aligned}\)

\(\begin{aligned}{c}5.34 \times {10^5}\;{\rm{\mu m}} = 5.34 \times {10^5}\;{\rm{\mu m}} \times \frac{{{{10}^{ - 6}}\;{\rm{m}}}}{{{\rm{1}}\;{\rm{\mu m}}}}\\ = 0.534\;{\rm{m}}\end{aligned}\)

Rule:

The final answer should not contain more decimal places than the number with the fewest decimal places when adding or subtracting numbers.

Now, adding the numbers, you get

\(\begin{aligned}{l}1.80\;{\rm{m}} + 142.5\;{\rm{cm}} + 5.34 \times {10^5}\;{\rm{m}}\\ = 1.80\;{\rm{m}} + 1.425\;{\rm{m}} + 0.534\;{\rm{m}}\\ = 3.759\;{\rm{m}}\end{aligned}\).

Here, the number with the fewest decimal places is 1.80 m.

So, there are two digits after the decimal point.

As there should be two digits after the decimal point, the significant figure representation of the sum will be 3.76.