Measurement - Operations with Lengths and Scale Diagrams

Calculate the total length of three ribbons measuring $45\ cm$, $1.2\ m$, and $850\ mm$. Give your answer in meters ($m$).

Convert all to meters: $45\ cm = \frac{45}{100} = 0.45\ m$ $1.2\ m = 1.2\ m$ $850\ mm = \frac{850}{1000} = 0.85\ m$ Sum: $0.45 + 1.2 + 0.85 = 2.5\ m$

To add different units of length, they must first be converted to the target unit (meters in this case). Using the conversion factors $100\ cm = 1\ m$ and $1000\ mm = 1\ m$, we sum the values.

Subtract $3.75\ m$ from $12\ m$ using vertical arithmetic.

$\begin{array}{r} 12.00 \\ - 3.75 \\ \hline 8.25 \end{array}$ Result: $8.25\ m$

We align the decimal points and perform the subtraction. Borrowing is required from the tens and ones place to subtract $0.75$ from $0.00$.

A map has a scale of $1:200,000$. If the distance between two cities on the map is $5.5\ cm$, what is the actual distance in kilometers ($km$)?

Actual distance in $cm$: $5.5 \times 200,000 = 1,100,000\ cm$ Convert $cm$ to $km$: $1,100,000 \div 100 = 11,000\ m$ $11,000 \div 1000 = 11\ km$

Multiply the drawing distance by the scale factor to find the actual distance in $cm$. Then, convert $cm$ to $m$ by dividing by $100$, and finally $m$ to $km$ by dividing by $1000$.

A room is $6\ m$ long. If you are drawing a floor plan with a scale of $1:50$, how long should the line for the room be on your paper?

Actual length in $cm$: $6\ m \times 100 = 600\ cm$ Drawing length: $\frac{600}{50} = 12\ cm$

First, convert the actual length into a unit easier to draw (centimeters). Then, divide the actual length by the scale factor ($50$) to find the corresponding length on the diagram.