Question

decide whether each statement is true or false.
statement: if $p$ is a single-digit number, then $p \times 10^{3}$ is always less than $10^{4}$.
true/false options: true, false

Explanation:

Step1: Define single-digit range

Single-digit $p$: $1\leq p\leq9$ (positive integers, as 0 would make $p\times10^3=0$ which is still less, but we test max $p$)

Step2: Calculate max $p\times10^3$

$\max(p\times10^3)=9\times10^3=9000$

Step3: Compare to $10^4$

$10^4=10000$, and $9000<10000$

Answer:

True