Let's go through each expression on the left and find its equivalent expression on the right, step-by-step:
1. [tex]$6.038 \cdot 100$[/tex]
- When you multiply 6.038 by 100, you shift the decimal point two places to the right.
- This means [tex]$6.038 \cdot 100 = 603.8$[/tex]
- Therefore, [tex]$6.038 \cdot 100$[/tex] matches with [tex]$603.8$[/tex]
2. [tex]$603.8 \div 10$[/tex]
- Dividing 603.8 by 10 shifts the decimal point one place to the left.
- This means [tex]$603.8 \div 10 = 60.38$[/tex]
- Therefore, [tex]$603.8 \div 10$[/tex] matches with [tex]$60.38$[/tex]
3. [tex]$60.38 \div 1,000$[/tex]
- Dividing 60.38 by 1,000 shifts the decimal point three places to the left.
- This means [tex]$60.38 \div 1,000 = 0.06038$[/tex]
- Therefore, [tex]$60.38 \div 1,000$[/tex] matches with [tex]$0.06038$[/tex]
4. [tex]$0.6038 \cdot 10$[/tex]
- Multiplying 0.6038 by 10 shifts the decimal point one place to the right.
- This means [tex]$0.6038 \cdot 10 = 6.038$[/tex]
- Therefore, [tex]$0.6038 \cdot 10$[/tex] matches with [tex]$6.038$[/tex]
So the matches are:
[tex]\[
\begin{array}{ll}
6.038 \cdot 100 & 603.8 \\
603.8 \div 10 & 60.38 \\
60.38 \div 1,000 & 0.06038 \\
0.6038 \cdot 10 & 6.038 \\
\end{array}
\][/tex]
