Question

Marsha thinks that because 123 is greater than 68, 0.123 must be greater than 0.68. Show and explain why Marsha is incorrect.

Answer 1

Let's begin by listing out the information given to us:

`\begin{gathered} 123=1\text{0}0 \\ \text{ 20} \\ \text{ 3} \\ 123=1\text{ hundred + 2 tens + 3 units} \\ 68\text{ = 6 (10)} \\ \text{ 8} \\ 68\text{ = 6 tens + 8 units} \end{gathered}`

To know which is greater between 0.123 To know which i3& 0.68, let's express it in tenth, hundredth & thousandth

`\begin{gathered} 0.123=3\text{ thousandth + 2 hundredth + 1 tenth + 0 unit} \\ 0.123=0.003+0.02+0.1+0 \\ 0.68=\text{ 6 hundredth + 8 tenth + 0 unit} \\ 0.68=0.60+0.08+0 \end{gathered}`

0.123 has 3 decimal places, which means it is 123/1000

0.68 has 2 decimal places, which means it is 68/100

When you multiply by 100, we have:

0.123 * 100 = 12.3

0.68 * 100 = 68

It becomes very evident that 0.68 is greater than 0.123