133 is 0.7​% of what​ number? Use pencil and paper. Would you expect the answer to be a lot less than 133​, slightly less than 133​, slightly greater than 133​, or a lot greater than 133​? Explain.

Part 1
133 is 0.7​% of__.
​(Type an integer or a​ decimal.)

1 answer

To solve the problem, we start with the formula for finding a number when we know its percentage. If \( x \) is the number we want to find, we can express the relationship as:

\[ 133 = 0.7% \text{ of } x \]

This can be rewritten as:

\[ 133 = \frac{0.7}{100} \times x \]

To isolate \( x \), we can rearrange the equation:

\[ x = \frac{133 \times 100}{0.7} \]

Now, let's calculate that step by step:

  1. First calculate \( 133 \times 100 \): \[ 133 \times 100 = 13300 \]

  2. Next, divide by \( 0.7 \): \[ x = \frac{13300}{0.7} \]

    To perform the division, you can rewrite \( 0.7 \) as \( \frac{7}{10} \): \[ x = 13300 \div 0.7 = 13300 \times \frac{10}{7} = \frac{133000}{7} \]

  3. Now perform the division \( 133000 \div 7 \): \[ 133000 \div 7 = 19000 \]

Thus,

\[ x \approx 19000 \]

Therefore:

Part 1: 133 is 0.7% of 19000.

Explanation of Expectation

To determine whether we would expect this answer to be a lot less than 133, slightly less, slightly greater, or a lot greater than 133:

Since 0.7% is a small percentage, we would anticipate that the total (which is the number we are calculating) should be considerably greater, because 0.7% of an amount represents just a fraction of that amount. This logic leads us to conclude that the resulting number (19000) is indeed a lot greater than 133.