Question

1. consider the expressions.

600 × 100 ml 600 × 10³ ml 6 × 10² × 1,000 ml
a. circle the expression that does not represent how to convert 600 liters to milliliters.
b. explain your choice.

Explanation:

Part a

To determine which expression does not represent converting 600 liters to milliliters, we first recall the conversion factor: \(1\) liter \( = 1000\) milliliters or \(1\mathrm{L}=10^{3}\mathrm{mL}\).

Let's analyze each expression:

1. For \(600\times100\mathrm{mL}\):

• Calculate the value: \(600\times100 = 60000\mathrm{mL}\). But \(600\) liters should be \(600\times1000 = 600000\mathrm{mL}\) (since \(1\mathrm{L} = 1000\mathrm{mL}\)).

1. For \(600\times10^{3}\mathrm{mL}\):

• Since \(10^{3}=1000\), then \(600\times10^{3}=600\times1000 = 600000\mathrm{mL}\), which is the correct conversion for \(600\) liters.

1. For \(6\times10^{2}\times1000\mathrm{mL}\):

• First, \(6\times10^{2}=600\), so \(6\times10^{2}\times1000=600\times1000 = 600000\mathrm{mL}\), which is also the correct conversion for \(600\) liters.

So the expression that does not represent the conversion is \(600\times100\mathrm{mL}\). We would circle \(600\times100\mathrm{mL}\).

Part b

The conversion factor between liters and milliliters is \(1\) liter \( = 1000\) milliliters (or \(1\mathrm{L}=10^{3}\mathrm{mL}\)). To convert \(600\) liters to milliliters, we use the formula: \(\text{Volume in mL}=\text{Volume in L}\times1000\) (or \(\text{Volume in mL}=\text{Volume in L}\times10^{3}\)).

• For \(600\times10^{3}\mathrm{mL}\), since \(10^{3} = 1000\), this is equivalent to \(600\times1000\mathrm{mL}\), which is correct.
• For \(6\times10^{2}\times1000\mathrm{mL}\), \(6\times10^{2}=600\), so this is also \(600\times1000\mathrm{mL}\), which is correct.
• For \(600\times100\mathrm{mL}\), \(100

eq1000\) (the correct conversion factor), so \(600\times100\mathrm{mL}=60000\mathrm{mL}\), while \(600\) liters should be \(600000\mathrm{mL}\). Thus, \(600\times100\mathrm{mL}\) does not represent the conversion.

Final Answers

a. Circle \(600\times100\mathrm{mL}\)

b. As explained above, \(600\times100\mathrm{mL}\) uses a conversion factor of \(100\) (instead of \(1000\) or \(10^{3}\)) and does not give the correct volume in milliliters for \(600\) liters.

Answer:

The conversion factor between liters and milliliters is \(1\) liter \( = 1000\) milliliters (or \(1\mathrm{L}=10^{3}\mathrm{mL}\)). To convert \(600\) liters to milliliters, we use the formula: \(\text{Volume in mL}=\text{Volume in L}\times1000\) (or \(\text{Volume in mL}=\text{Volume in L}\times10^{3}\)).

• For \(600\times10^{3}\mathrm{mL}\), since \(10^{3} = 1000\), this is equivalent to \(600\times1000\mathrm{mL}\), which is correct.
• For \(6\times10^{2}\times1000\mathrm{mL}\), \(6\times10^{2}=600\), so this is also \(600\times1000\mathrm{mL}\), which is correct.
• For \(600\times100\mathrm{mL}\), \(100

eq1000\) (the correct conversion factor), so \(600\times100\mathrm{mL}=60000\mathrm{mL}\), while \(600\) liters should be \(600000\mathrm{mL}\). Thus, \(600\times100\mathrm{mL}\) does not represent the conversion.

Final Answers

a. Circle \(600\times100\mathrm{mL}\)

b. As explained above, \(600\times100\mathrm{mL}\) uses a conversion factor of \(100\) (instead of \(1000\) or \(10^{3}\)) and does not give the correct volume in milliliters for \(600\) liters.