Is 0.117 less than 0.5?

Feb 22, 2018

Yes.

Explanation:

The easiest thing to do is to look at both numbers to $1 d . p$
$0.117 = 0.1$ to $1 d . p$
$0.5$ is already is $1 d . p$

1 is less than 5

$\therefore 0.1 < 0.5$

Feb 22, 2018

$0.117 < 0.500$

Explanation:

If you write the numbers with the same number of decimal places it is easier to see the relationship between them.

Compare $0.117 \mathmr{and} 0.500$

Clearly $117 < 500$

Students tend to forget that $0.5 = 0.50 = 0.500$

You are not comparing $117$ with $5$

Looking at just the first decimal place would have been enough.

$0.1 < 0.5$

$\frac{1}{10} < \frac{5}{10}$

$1 < 5$

Feb 23, 2018

This is a sort of trick showing how you can 'play' with numbers to give you what you whant.

Explanation:

Using the following principle

$\frac{1}{4} = \left(\frac{1}{4} \times 1\right) \equiv \left(\frac{1}{4} \times \frac{2}{2}\right) = \frac{2}{8} \leftarrow \text{ All the same value}$

If $0.117$ is less than $0.5$ then $\frac{0.117}{0.5}$ will be less than 1

$\left(\frac{0.117}{0.5} \times 1\right) \equiv \left(\frac{0.117}{0.5} \times \frac{100}{100}\right) = \frac{117}{500} < 1$

As $117$ is less than $500$ then $0.117$ is less than $0.5$

Notice that 'Ez as pi' has used the same approach but with different numbers.