example
Nick ran a [latex]\text{10-kilometer}[/latex] race. How many meters did he run?
(credit: William Warby, Flickr)
Solution
We will convert kilometers to meters using the Identity Property of Multiplication and the equivalencies in the reference table from earlier.
|
[latex]10[/latex] kilometers |
Multiply the measurement to be converted by [latex]1[/latex]. |
[latex]10 \color{red}{km}\cdot 1[/latex] |
Write [latex]1[/latex] as a fraction relating kilometers and meters. |
[latex]10 \color{red}{km}\cdot \frac{1000 m}{1\color{red}{km}}[/latex] |
Simplify. |
[latex]\frac{10\color{red}{km}\cdot 1000 m}{1\color{red}{km}}[/latex] |
Multiply. |
[latex]10,000[/latex] m |
|
Nick ran [latex]10,000[/latex] meters. |
example
Eleanor’s newborn baby weighed [latex]3200[/latex] grams. How many kilograms did the baby weigh?
Answer:
Solution
We will convert grams to kilograms.
|
[latex]3200 \color{red}{grams}[/latex] |
Multiply the measurement to be converted by [latex]1[/latex]. |
[latex]3200 \color{red}{g}\cdot 1[/latex] |
Write [latex]1[/latex] as a fraction relating kilograms and grams. |
[latex]3200 \color{red}{g}\cdot \frac{1 kg}{1000 \color{red}{g}}[/latex] |
Simplify. |
[latex]3200 \color{red}{g}\cdot \frac{1 kg}{1000 \color{red}{g}}[/latex] |
Multiply. |
[latex]\frac{3200 kilograms}{1000}[/latex] |
Divide. |
[latex]3.2[/latex] kilograms |
|
The baby weighed [latex]3.2[/latex] kilograms. |
example
Convert: 1. [latex]350[/latex] liters to kiloliters 2. [latex]4.1[/latex] liters to milliliters.
Answer:
Solution
1. We will convert liters to kiloliters. In the reference table, we see that [latex]\text{1 kiloliter}=\text{1000 liters}[/latex].
|
[latex]350[/latex] L |
Multiply by [latex]1[/latex], writing [latex]1[/latex] as a fraction relating liters to kiloliters. |
[latex]350 L \cdot \frac{1 kl}{1000 L}[/latex] |
Simplify. |
[latex]350 \color{blue}{L} \cdot \frac{1 kl}{1000 \color{blue}{L}}[/latex] |
Move the decimal [latex]3[/latex] units to the left. |
|
|
[latex]0.35[/latex] kL |
2. We will convert liters to milliliters. In the reference table, we see that [latex]\text{1 liter}=1000\text{milliliters.}[/latex]
|
[latex]4.1[/latex] L |
Multiply by [latex]1[/latex], writing [latex]1[/latex] as a fraction relating milliliters to liters. |
[latex]4.1 L \cdot \frac{1000 ml}{1 L}[/latex] |
Simplify. |
[latex]4.1 L \color{blue}{L} \cdot \frac{1000 ml}{1 \color{blue}{L}}[/latex] |
Move the decimal [latex]3[/latex] units to the right. |
|
|
[latex]4100[/latex] mL |
example
Ryland is [latex]1.6[/latex] meters tall. His younger brother is [latex]85[/latex] centimeters tall. How much taller is Ryland than his younger brother?
Answer:
Solution
We will subtract the lengths in meters. Convert [latex]85[/latex] centimeters to meters by moving the decimal [latex]2[/latex] places to the left; [latex]85[/latex] cm is the same as [latex]0.85[/latex] m.
Now that both measurements are in meters, subtract to find out how much taller Ryland is than his brother.
[latex-display]\begin{array}{}\\ \\ \hfill \text{1.60 m}\\ \hfill \underset{\text{_______}}{\text{-0.85 m}}\\ \hfill \text{0.75 m}\end{array}[/latex-display]
Ryland is [latex]0.75[/latex] meters taller than his brother.
example
Dena’s recipe for lentil soup calls for [latex]150[/latex] milliliters of olive oil. Dena wants to triple the recipe. How many liters of olive oil will she need?
Answer:
Solution
We will find the amount of olive oil in milliliters then convert to liters.
|
Triple [latex]150[/latex] mL |
Translate to algebra. |
[latex]3\cdot 150\text{mL}[/latex] |
Multiply. |
[latex]450\text{mL}[/latex] |
Convert to liters. |
[latex]450\text{mL}\cdot \frac{0.001\text{L}}{1\text{mL}}[/latex] |
Simplify. |
[latex]0.45\text{L}[/latex] |
|
Dena needs [latex]0.45[/latex] liter of olive oil. |