Chapter 2.3, Problem 37PP

Interpretation Introduction

Interpretation:

Numbers 10, 100 and 1000 are to be presented in scientific notations with 2, 3 and 4 significant figures, respectively.

Concept introduction:

Numbers that are too large or too small are represented by an exponential format called scientific notations for convenience.

Scientific notations are generally expressed as follows:

$\text{m}{\text{×10}}^{\text{n}}$

Where,

• n is the number of places the decimal has moved and is known as an exponent.
• m is the number.

An example is 55000 is represented as $5.5\times {10}^4$.

To exactly determine the uncertainty in final answer of a measurement, significant digits are calculated.

The rules for counting the significant digits will be as follows:

• Numbers that are non-zero are significant digits.
• The zeros preceding numbers that are non-zero are non-significant as they only define the place of decimal.
• The zeros in between numbers that are non-zero are also significant.
• The zeros after numbers that are non-zero are significant only if the decimal is present in the number.

Answer to Problem 37PP

Numbers 10, 100 and 1000 in scientific notations with 2, 3 and 4 significant figures, respectively, are $1.0\times {10}^1$, $1.00\times {10}^2$ and $1.000\times {10}^3$.

Explanation of Solution

Numbers 10, 100 and 1000 in scientific notations with 2, 3 and 4 significant figures, respectively can be represented as follows:

$\begin{array}{l}10=1.0\times {10}^1\\ 100=1.00\times {10}^2\\ 1000=1.000\times {10}^3\end{array}$

Conclusion

Numbers 10, 100 and 1000 in scientific notations with 2, 3 and 4 significant figures, respectively, are $1.0\times {10}^1$, $1.00\times {10}^2$ and $1.000\times {10}^3$.