Scale Factor as a Percent
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Learning text on the topic Scale Factor as a Percent
Scale Factor as a Percent – Definition
In many real-world applications, such as creating scale models or reading maps, understanding the concept of scale factor is crucial. A scale factor is a number which scales, or adjusts, the dimensions of a figure.
Scale Factor as a Percent represents how much a known size has been increased or decreased to reach a new size, expressed as a percentage.
| Scaling Direction | Description | |
|---|---|---|
| Scaling Up | Enlarging an object to a size greater than its original. Commonly used in model building where details need to be visible at a larger scale. | |
| Scaling Down | Reducing an object to a size smaller than its original. Used in situations like map making where large areas need to be represented on a smaller, manageable scale. |
Understanding Scale Factor as a Percent – Explanation
Scale factors are often given in various forms, such as ratios or fractions, but converting these to a percent makes comparisons and calculations easier, especially in practical situations like resizing images or blueprints and learning how to create a scale drawing.
To convert a scale factor from a ratio or fraction to a percentage, you simply multiply it by $100$.
Scale Factor as a Percent – Step-by-Step Process
Converting a scale factor into a percentage can be useful in understanding how much an object’s size has been changed in models, drawings, or maps. Here’s a step-by-step breakdown of how to convert a scale factor, given as a fraction or ratio, into a percent:
Identify the Scale Factor: First, determine the scale factor used in the scaling. It is usually given as a ratio or fraction (e.g., $1:25$ or $1/25$).
Convert the Ratio or Fraction to a Decimal:
- If the scale factor is a ratio (like $1:25$), convert it to a fraction $\frac{1}{25}$).
- To convert a fraction to a decimal, divide the numerator by the denominator $\frac{1}{25} = 0.04$).
Convert the Decimal to a Percentage:
- Multiply the decimal by $100$ to convert it to a percentage ($0.04 \times$] 100$ = $4$%).
Interpret the Result:
- A result of 4% means the scaled object is 4% the size of the original.
Here are more examples of scale factors and their conversion to a percentage.
| Scale Factor | Percentage |
|---|---|
| $1:1$ | $100\%$ |
| $1:2$ | $50\%$ |
| $1:5$ | $20\%$ |
| $1:10$ | $10\%$ |
| $1:20$ | $5\%$ |
| $1:50$ | $2\%$ |
| $1:100$ | $1\%$ |
| $1:200$ | $0.5\%$ |
| $2:1$ | $200\%$ |
Scale Factor as a Percent – Example or Practice
Practise some on your own!
Scale Factor as a Percent – Summary
Key Learnings from this Text:
- Scale factor simplifies understanding proportions in models and maps.
- Converting scale factors to percentages aids in easy and practical application.
- The process involves converting the ratio or fraction to a decimal and then to a percentage.
Scale Factor as a Percent – Frequently Asked Questions
Scale Factor as a Percent exercise
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Increasing Dimensions.
HintsAn increase of $600$% means we would multiply by $\frac{600}{100} = 6$. Therefore, the scale factor is $6$.
An increase of $70$% means we would multiply by $\frac{70}{100} = 0.7$. Therefore, the scale factor is $0.7$.
Solution- An increase of $500$% means we multiply by $\frac{500}{100} = 5$. The scale factor would be $5$ as shown above.
- $200$% $=$ Scale factor $2$
- $75$% $=$ Scale factor $0.75$
- $750$% $=$ Scale factor $7.5$
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Determine the correct conditions to produce a distortion.
HintsAn object is distorted if the dimensional increase (scale factor) of the vertical is not the same as the one on the horizontal.
For example, a horizontal dimension increase of $900$% and vertical dimension increase of $500$% would cause a distortion as the scale factors are $9$ and $5$. It could look something like this.
When the scale factor is the same for the vertical and the horizontal the enlargement is not distorted.
For example, a scale factor of $5$ on both vertical and horizontal will not be distorted.
There are $3$ correct answers here.
SolutionThe following would cause a distortion as the vertical and horizontal scale increases are not equal:
- Horizontal dimension increase $40$% and vertical dimension increase $400$%. (See this one above)
- Horizontal dimension increase $400$% and vertical dimension increase $500$%.
- Horizontal dimension increase $250$% and vertical dimension increase $350$%.
The other two have the same increase on the vertical and horizontal so they will not be distorted.
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Find the correct dimensions.
HintsHorizontal is across and vertical is up and down.
For example:
For a stretch of $700$% we multiply the side by a scale factor of $7$.
For a shrink of $\frac{1}{5}$ we multiply the side by a scale factor of $0.2$.
SolutionThe correct dimensions are horizontally $15$ m and vertically $1$ m.
- Horizontal scale factor is $3$, we multiply $3\times5 = 15$ m.
- Vertical scale factor is $0.25$, we multiply $4\times0.25 = 1$ m.
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Find the dimensions of a distorted photograph.
HintsHorizontal is across and vertical is up and down.
- For a stretch of $700$% we multiply the side by a scale factor of $7$.
- For a shrink of $35$% we multiply the side by a scale factor of $0.35$.
Multiply each side by the scale factor for the new dimensions.
SolutionThe correct answer is horizontal $6$ ft and vertical $12$ ft.
- A horizontal shrink of scale factor $0.75$ means, $0.75\times8 = 6$ ft.
- A vertical stretch of scale factor $3$ means, $3\times4 = 12$ ft.
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Use scale factor to increase an item.
HintsAn increase of $500$% is a scale factor of $5$.
Therefore, an increase of $200$% is a scale factor of ?
When we have worked out the scale factor we multiply each side by this scale factor.
As an example, if we had a side length of $2$m with a scale factor of $6$, we would multiply $2\times6 = 12$ to get the new length.
For example, this rectangle can be increased by $400$%.
- $400$% $=$ a scale factor of $4$
- Multiply the width and height by $4$
- The new dimensions are $2\times4 = 8$m and $3\times4 = 12$m.
Solution- The correct dimensions are $6$ by $4$
- $200$% $=$ a scale factor of $2$
- Multiply the width and height by $2$
- The new dimensions are $2\times2 = 4$m and $3\times2 = 6$m
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Find the scale factors of the distortions.
HintsTo work out the scale factor, divide the corresponding side on B by the corresponding side on A.
For example here the scale factor is $8\div2 = 4$. Therefore, the stretch horizontally is $4 \times 100 = 400$%.
If the corresponding side on B is smaller then it is a shrink.
For example, here the scale factor is $\frac{2}{10} = \frac{1}{5}$. To find the percentage we multiply $100 \times \frac{1}{5} = 20$%.
SolutionGreen rectangles
- Horizontal stretch is $4\div2 = 2 = 200$%.
- Vertical shrink is $6\div8 = \frac{3}{4} = 75$%.
- Horizontal shrink is $2\div4 = \frac{1}{2} = 50$%.
- Vertical stretch is $9\div3 = 3 = 300$%.
- Horizontal stretch is $12\div3 = 4 = 400$%.
- Vertical shrink is $4\div5 = \frac{4}{5} = 80$%.
- Horizontal shrink is $3\div5 = \frac{3}{5} = 60$%.
- Vertical stretch is $10\div4 = 2.5 = 250$%.
