Questions: Express 0.00720 in exponential notation. that best completes the sentence 7.2 × 10^-3 7.2 × 10^3 7.20 × 10^-3 7.20 × 10^3 7.2000 × 10^-3

Transcript text: Express 0.00720 in exponential notation. that best completes the sentence $7.2 \times 10^{-3}$ $7.2 \times 10^{3}$ $7.20 \times 10^{-3}$ $7.20 \times 10^{3}$ $7.2000 \times 10^{-3}$

Solution

Solution Steps

Step 1: Identify the significant digits

The number $ 0.00720 $ has three significant digits: $ 7 $, $ 2 $, and $ 0 $. The trailing zero is significant because it is explicitly written.

Step 2: Move the decimal point to the right of the first non-zero digit

Move the decimal point in $ 0.00720 $ to the right of the first non-zero digit $ 7 $, resulting in $ 7.20 $. This requires moving the decimal point three places to the right.

Step 3: Determine the exponent

Since the decimal point was moved three places to the right, the exponent is $ -3 $. This is because the original number is less than 1.

Step 4: Write the number in exponential notation

Combine the significant digits with the exponent to express the number in exponential notation: $ 7.20 \times 10^{-3} $.