Question

How are 0.22 and 0.022 the values of the digit 2 related

Answer 1

Answer:

$0.022 = \displaystyle\frac{1}{10}\times 0.22\\\\=\displaystyle\frac{1}{10}\times (\frac{2}{10} + \frac{2}{100})\\\\=\displaystyle\frac{2}{100} + \frac{2}{1000}$          

Step-by-step explanation:

We are given the following in the question:

0.22 and 0.22

We have to compare the values of 2 in the given numbers.

Expanding the given numbers we have,

$0.22 = 0 + \displaystyle\frac{2}{10} + \frac{2}{100}\\\\0.022 = 0 + \frac{2}{100} + \frac{2}{1000}$

In 0.22 the first two appears at the tenths position followed ny another 2 whereas in 0.022, the first 2 appears on the hundredths position followed by another 2

Thus, if we compare the values

$0.22 > 0.022\\\text{Comparing 2's, we get}\\\\\displaystyle\frac{2}{10} + \frac{2}{100} > \frac{2}{100} + \frac{2}{1000}$.

Relation:

$0.022 = \displaystyle\frac{1}{10}\times 0.22\\\\=\displaystyle\frac{1}{10}\times (\frac{2}{10} + \frac{2}{100})\\\\=\displaystyle\frac{2}{100} + \frac{2}{1000}$

Answer 2

0.22 is ten times larger than 0.022.