Question

The power of $10$ to make the following true is .
$6.4\times {10}^{?}=6,400$

• A. $0$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is B $3$

$\underset{–}{\text{Need to find:}}$ The exponent $(?)$ in $6.4\times {10}^{?}=6,400$

$\bullet$ Multiplying by $10={10}^1$: Decimal point moves $1$ unit to the right, i.e.,
$6.4\times 10=64.0=64$

$\bullet$ Multiplying by $100={10}^2$: Decimal point moves $2$ units to the right, i.e.,
$6.4\times 100=640.0=640$

$\bullet$ Multiplying by $1,000={10}^3$: Decimal point moves $3$ units to the right, i.e.,
$\underset{–}{6.4\times 1,000=6,400.0=6,400}$

$\therefore 6.4\times 1,000=\underset{–}{6.4\times {10}^3=6,400.0=6,400}$

Hence, the exponent $(?)$ in $6.4\times {10}^{?}=6,400$ is $\underset{–}{3}$.