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Difficulty: MediumConverting Between Fractions, Decimals, and Percents

A machinist is adjusting the feed rate on a lathe. The machine is currently operating at 0.180.18 of its maximum safe speed. The technical manual specifies that for the selected alloy, the speed must be increased to exactly 2150\frac{21}{50} of the maximum safe speed. By what percentage of the maximum safe speed must the current speed be increased?

  1. A
    3%
  2. B
    4.2%
  3. 24%Answer
  4. D
    42%

Answer

24%
To find the required increase, both the current speed and the target speed must be in the same format. Converting the current speed to a percent yields 18% (0.18 * 100). Converting the target speed to a percent yields 42% (21/50 = 42/100 = 42%). The difference between the target speed and the current speed is 42% - 18% = 24%.

Step-by-Step Solution

1
Convert the current operating speed from a decimal to a percentage.
0.18=18%0.18 = 18\%
Converting all values to percentages makes them easy to compare and subtract.
2
Convert the target operating speed from a fraction to a percentage.
2150=42100=42%\frac{21}{50} = \frac{42}{100} = 42\%
The target speed must also be a percentage to find the precise difference.
3
Subtract the current percentage from the target percentage to find the required increase.
42%−18%=24%42\% - 18\% = 24\%
The difference between the two values reveals how much the speed needs to be increased.

Key Concept

Converting fractions and decimals to percentages to determine the difference between two values.
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Topics

Converting Between Fractions, Decimals, and Percents

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