Question

The standard form for $234000000$ is

• A. $2.34\times {10}^8$
• B. $0.234\times {10}^9$
• C. $2.34\times {10}^{-8}$
• D. $0.234\times {10}^{-9}$

Answer 1

The correct option is A

$2.34\times {10}^8$

Any number can be expressed as decimal numbers between 1 and 10 multiplied by a power of 10. This form of representation is termed as the standard form.

$$\begin{gathered} 234000000=234\times 1000000 \\ 234000000=2.34\times 100\times {10}^6 \\ 234000000=2.34\times {10}^2\times {10}^6 \end{gathered}$$

By laws of exponent,

$x^m\times x^n=x^{m+n}$

$$\begin{gathered} 234000000=2.34\times {10}^{(2+6)} \\ 234000000=2.34\times {10}^8 \end{gathered}$$

Hence, the standard form for $234000000$ is $2.34\times {10}^8$.