Question

multiply.
30 × 2,000 = \boxed{}

Explanation:

Step1: Analyze the numbers

We have \(30\) and \(2000\). We can rewrite \(30\) as \(3\times10\) and \(2000\) as \(2\times1000\) (or \(2\times10^{3}\)).

Step2: Multiply the non - power - of - ten parts first

Multiply \(3\) and \(2\): \(3\times2 = 6\).

Step3: Multiply the powers of ten

Multiply \(10\) (from \(30 = 3\times10\)) and \(1000\) (from \(2000=2\times1000\)). Using the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), \(10\times1000=10^{1}\times10^{3}=10^{1 + 3}=10^{4}=10000\).

Step4: Combine the results

Multiply the result from Step 2 and Step 3: \(6\times10000 = 60000\). We can also do it by counting the number of zeros. \(30\) has 1 zero and \(2000\) has 3 zeros. So in total, there are \(1 + 3=4\) zeros. Then \(3\times2 = 6\), so the number is \(6\) followed by 4 zeros, which is \(60000\).

Answer:

\(60000\)