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Convert 186 centimeters to meters using dimensional analysis.

Begin by writing 186 centimeters as a fraction:

[tex]\[ \frac{186 \, \text{cm}}{1} \][/tex]

Answer :

To convert 186 centimeters to meters using dimensional analysis, follow these steps:

1. Write 186 centimeters as a fraction:
[tex]\[
\frac{186 \ \text{cm}}{1}
\][/tex]

2. Use the conversion factor between centimeters and meters:
- We know that 1 meter is equal to 100 centimeters. Therefore, the conversion factor is:
[tex]\[
\frac{1 \ \text{m}}{100 \ \text{cm}}
\][/tex]

3. Set up the dimensional analysis:
- Multiply the given value by the conversion factor so that the centimeters units will cancel out, leaving you with meters:
[tex]\[
\frac{186 \ \text{cm}}{1} \times \frac{1 \ \text{m}}{100 \ \text{cm}}
\][/tex]

4. Perform the multiplication:
- Multiply the numbers:
[tex]\[
186 \times \frac{1}{100} = 1.86
\][/tex]

5. Cancel out the units and write the result:
- The centimeters unit ([tex]\(\text{cm}\)[/tex]) cancels out, leaving you with meters ([tex]\(\text{m}\)[/tex]). Thus, you have:
[tex]\[
1.86 \ \text{m}
\][/tex]

The final result is that 186 centimeters is equal to 1.86 meters.

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