Question

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.)

Answer 1

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**.