Question

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

Answer 1

0.22 is ten times larger than 0.022.

Answer 2

`0.022 = \displaystyle(1)/(10)* 0.22\\\\=\displaystyle(1)/(10)* ((2)/(10) + (2)/(100))\\\\=\displaystyle(2)/(100) + (2)/(1000)`

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(2)/(10) + (2)/(100)\\\\0.022 = 0 + (2)/(100) + (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(2)/(10) + (2)/(100) > (2)/(100) + (2)/(1000)`.

Relation:

`0.022 = \displaystyle(1)/(10)* 0.22\\\\=\displaystyle(1)/(10)* ((2)/(10) + (2)/(100))\\\\=\displaystyle(2)/(100) + (2)/(1000)`