Question

What is the exponent $(\ast )$ in $1.3\times {10}^{\ast }=13,000?$

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is B $4$

$\underset{–}{\text{Need to find:}}$ The exponent $(\ast )$ in $1.3\times {10}^{\ast }=13,000$

$\bullet$ Multiplying by $10={10}^1$: Decimal point moves $1$ unit to the right, i.e.,
$1.3\times 10=13.0=13$

$\bullet$ Multiplying by $100={10}^2$: Decimal point moves $2$ units to the right, i.e.,
$1.3\times 100=130.0=130$

$\bullet$ Multiplying by $1,000={10}^3$: Decimal point moves $3$ units to the right, i.e.,
$1.3\times 1,000=1,300.0=1,300$

$\bullet$ Multiplying by $10,000={10}^4$: Decimal point moves $4$ units to the right, i.e.,
$\underset{–}{1.3\times 10,000=13,000.0=13,000}$

$\therefore 1.3\times 10,000=\underset{–}{1.3\times {10}^4=13,000.0=13,000}$

Hence, the exponent $(\ast )$ in $1.3\times {10}^{\ast }=13,000$ is $\underset{–}{4}$, i.e., option (b.) is the correct one.