Question

30 is 0.2% of what number? use pencil and paper. would you expect the answer to be a lot less than 30, slightly less than 30, slightly greater than 30, or a lot greater than 30? explain.
30 is 0.2% of \boxed{}
(type an integer or a decimal.)

Explanation:

Step1: Recall the percentage formula

Let the number be \( x \). We know that \( \text{Percentage} \times \text{Number} = \text{Part} \). Here, the percentage is \( 0.2\% \) which is \( 0.002 \) in decimal, the part is \( 30 \), and we need to find \( x \). So the formula becomes \( 0.002 \times x = 30 \).

Step2: Solve for \( x \)

To find \( x \), we divide both sides of the equation by \( 0.002 \). So \( x=\frac{30}{0.002} \). Calculating this, \( 30\div0.002 = 15000 \).

For the expectation part: Since \( 0.2\% \) is a very small percentage (less than \( 1\% \)), to get \( 30 \) as a part of a number, the number must be a lot greater than \( 30 \) because a small fraction (percentage) of a large number gives \( 30 \).

Answer:

For the box: \( 15000 \)

For the expectation: The answer is a lot greater than 30 because 0.2% is a very small percentage, so the whole number (of which 30 is 0.2%) must be much larger than 30.