Chapter SH, Problem 9.5.16EP

To determine

The number $0.00546$ needs to express in scientific notation.

Answer to Problem 9.5.16EP

The number $0.00546$ in scientific notation is $5.46\times {10}^{-3}$ .

Explanation of Solution

Given:

  $0.00546$

Concept Used:

To write the very large or very small numbers easily, the scientific notation is used. When any number between $1$ and $10$ which is multiplied with the power of $10$ then the scientific notations are in use.

The formula used to reconstruct the number into scientific notation is:

  $SN=a\times {10}^b$

Where,

New number: $a$

Decimal count: $b$

Calculation:

The given number is: $0.00546$

Take the given number and move a decimal place to the right position so there is non-zero point. Get that:

Original number: $0.00546$

New number: $5.46$

Need to count the number of places the decimal point is moved:

New number: $5.46$

Decimal count: $b=3$

Now, reconstruct the number by using the formula of scientific notation:

  $\begin{array}{l}0.00546=a\times {10}^b\\ 0.00546=5.46\times {10}^{-3}\end{array}$

Conclusion:

Hence, $0.00546=5.46\times {10}^{-3}$ .