Question

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

Short answer

The value of the sum is 3.76 m

Step-by-step solution

Converting all numbers in the same unit

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,

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

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

Applying the rule of addition for significant figures

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.