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Chapter 6: Problem 26

Find decimal notation. $$ 93 \frac{1}{8} \% $$

Short Answer

Expert verified
0.93125

Step by step solution

01

Convert Mixed Number to Improper Fraction

Convert the mixed number in the percentage to an improper fraction. In this case, convert 93 \( \frac{1}{8} \) to (93 * 8 + 1) / 8 = \( \frac{745}{8} \).
02

Convert Fraction to Decimal

Divide the numerator by the denominator to convert the improper fraction to a decimal. Here, calculate \( \frac{745}{8} \) which equals 93.125.
03

Convert Percentage to Decimal

Divide the decimal obtained by 100 to find the decimal notation of the given percentage. Here, 93.125 divided by 100 equals 0.93125.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mixed Number Conversion
A mixed number combines a whole number and a fraction, like 93 and 1/8 in our example. Converting this into an improper fraction simplifies the calculations.
To convert a mixed number:
  • Multiply the whole number by the denominator of the fraction.
  • Add the numerator of the fraction to this product.
  • Write the sum over the original denominator.
So for 93 1/8:
  • Multiply 93 by 8 (denominator): 93 * 8 = 744
  • Add 1 (numerator): 744 + 1 = 745
  • Therefore, 93 1/8 converts to the improper fraction 745/8.
Improper Fractions
An improper fraction has a numerator larger than or equal to its denominator.
Another way of saying this is that the fraction is 鈥榯op-heavy鈥�. Improper fractions often arise when converting mixed numbers.
In our example:
  • The improper fraction is 745/8.
  • To convert this to a decimal, divide 745 by 8.

Dividing 745 by 8 gives us: \[ \frac{745}{8} = 93.125 \]
Percentage to Decimal Conversion
Percentages are another way to express fractions.
They are based on 100, so converting a percentage to a decimal is straightforward.
Just divide the percentage by 100.
For instance, 93.125% converts to a decimal by performing: 93.125 divided by 100, which is 0.93125.

This allows you to easily switch between percentages and decimals in various calculations.
Remember, move the decimal point two places to the left when converting from a percentage to a decimal.

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