Question

Which of the given options represents $0.00006589$ in scientific notation?

• A. $6.589\times {10}^{-6}$
• B. $65.89\times {10}^{-6}$
• C. $6589\times {10}^{-8}$
• D. $6.589\times {10}^{-5}$

Answer 1

The correct option is D $6.589\times {10}^{-5}$

Detailed step-by-step solution:
To write $0.00006589$ in $a\times {10}^n$ form, where $1\le a<10$, the decimal point will be shifted $5$ units to the right so the exponent of $10$ in its scientific notation will be $-5$ and the factor will be $6.589$.

$\Rightarrow 0.00006589=6.589\times {10}^{-5}$

Steps to write a number in scientific notation:
Step 1: Check whether the given number is between $0$ and $1$, or if the number is greater than or equal to $10$.

Step 2: If the number is greater than or equal to $10$, move the decimal point to the left and use the positive exponent.

Step 3: If the given number is between $0$ and $1$, move the decimal point to the right and use the positive exponent.



Alternatively
Representation of $0.00006589$ in exponential form:

$\Rightarrow 0.00006589=\frac{6589}{100,000,000}$ (in fraction)

$\Rightarrow 0.00006589=\frac{6589}{8}(\because {10}^8=100,000,000)$

$\Rightarrow 0.00006589=6589\times {10}^{-8}$ (by using the property of negative exponent, i.e.$\frac{1}{a^n}=a^{-n})$

Expressing $0.00006589$ in scientific notation:

$6589\times {10}^{-8}:$ It is in $a\times {10}^n$ form, but the factor $a=6589$ does not lie between $1$ and $10$. Hence, the number is not in scientific notation.

$\Rightarrow 6589=6.589\times 1000$

$\Rightarrow 6589=6.589\times {10}^3$

$\Rightarrow 0.00006589=6.589\times {10}^3\times {10}^{-8}$

$\Rightarrow 0.00006589=6.589\times {10}^{3-8}$ (by using the product rule of powers, i.e., $a^m\times a^n=a^{m+n}$)

$\Rightarrow 0.00006589=6.589\times {10}^{-5}$

The number which expresses $0.00006589$ in scientific notation is $6.589\times {10}^{-5}$