96 is 0.8​% of what​ number? Use pencil and paper. Would you expect the answer to be a lot less than 96​, slightly less than 96​, slightly greater than 96​, or a lot greater than 96​? Explain.

Question

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Part 1
96 is 0.8​% of
  
enter your response here.
​(Type an integer or a​ decimal.)

Answer 1

To find out what number 96 is 0.8% of, we can set up an equation. We'll denote the unknown number as \( x \).

The relationship can be expressed as: \[ 0.8% \text{ of } x = 96 \]

We can convert the percentage into a decimal: \[ 0.8% = \frac{0.8}{100} = 0.008 \]

Now, we can replace the percentage in the equation: \[ 0.008 \times x = 96 \]

Next, to find \( x \), we can divide both sides by 0.008: \[ x = \frac{96}{0.008} \]

Now, let's calculate that: \[ x = 96 \div 0.008 \] \[ x = 12000 \]

So, 96 is 0.8% of 12000.

Now, regarding the expectation of the answer relative to 96:

Since 0.8% is a small fraction, we would expect the number that 96 is 0.8% of to be significantly larger than 96. Hence, we would expect the answer to be a lot greater than 96. This is because when you're taking a small percentage of a number, that number has to be larger to yield a specific value (in this case, 96).