Chapter 1, Problem 19P

To determine

To express: The resultant sum with the correct number of significant figures.

Answer to Problem 19P

The sum with correct number of significant digits is 3.76 m.

Explanation of Solution

Given:

Formula used:

The conversion factors are,

1 m = 10⁶ micrometers,

1 cm = 10⁴ micrometers

Calculation:

Convert all the terms in micrometers. So, the sum is,

$1.80\text{m}+142.5\text{cm}+5.34\times {10}^5\mu \text{m}=180\text{m}\times \frac{{10}^6\mu \text{m}}{1\text{m}}+142.5\text{cm}\times \frac{{10}^4\mu \text{m}}{1\text{cm}}+5.34\times {10}^5\mu \text{m}$

              $=1.8\times {10}^6\mu \text{m}+142.5\times {10}^4\mu \text{m}+5.34\times {10}^5\mu \text{m}$

              $=(1.8\times 100+142.5+5.34\times 10)\times {10}^4\mu \text{m}$

              $=(180+142.5+53.4)\times {10}^4\mu \text{m}$

              $=375.9\times {10}^4\mu \text{m}$

Now, as the least number of significant figures in the terms of sum is three, so round off the answer to three significant digits. The sum becomes:

$376\times {10}^4\mu \text{m}$

Now, as the least number of decimal places in the terms was one, so change the power of the answer such that there is one decimal place in the final answer:

$37.6\times {10}^5\mu \text{m}=37.6\times {10}^5\times {10}^{-6}\text{m}$

      $=3.76\text{m}$

Conclusion:

The sum with correct number of significant digits is 3.76 m