Problem 77 - College Algebra Essentials

Question

Write each number in scientific notation. $$32,000$$

Step-by-Step Solution

Answer

The scientific notation of \(32,000\) is \(3.2 \times 10^4\).

Step 1: Identify the first non-zero digit

Look at the number \(32,000\). The first non-zero digit in this number is '3'. We want to rewrite this number so that it starts with the first non-zero digit.

Step 2: Place a decimal point after the first non-zero digit

Placing a decimal point after the first non-zero digit gives us \(3.2\). But we also need to represent all the remaining zeros.

Step 3: Count the number of places moved

Then count the number of places the decimal point was moved from the end of the number to its new position after the first non-zero digit. Here, the decimal point has moved 4 places to the left.

Step 4: Write the number in scientific notation

Write the number \(3.2\) multiplied by \(10\) to the power equal to the places moved i.e. \(4\). So, the scientific notation for \(32,000\) is \(3.2 \times 10^4\).