Problem 84 Write as a percent. Write the re... [FREE SOLUTION]

Chapter 6: Problem 84

Write as a percent. Write the remainder in fractional form. $$1 \frac{5}{9}$$

Short Answer

Expert verified

The mixed number $1 \frac{5}{9}$ expressed as a percent with remainder in fractional form is $156 \%$.

Step by step solution

Convert Mixed number to Decimal

First, convert the mixed number to a decimal. To do this, the fraction part of the mixed number $ \frac{5}{9} $ is divided. That gives approximately 0.56. Adding the whole number (1) to this value gives 1.56.

Convert Decimal to Percent

Now, to convert the decimal number to a percent, multiply by 100. This gives: $ 1.56 * 100 = 156 \% $.

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Key Concepts

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

Mixed Number Conversion

Mixed numbers consist of an integer part and a proper fraction part. Converting a mixed number to a decimal involves a simple step-by-step process:

First, focus on the fraction part of the mixed number. For example, in $1 \frac{5}{9}$, the fraction is $\frac{5}{9}$.
To convert this fraction to a decimal, perform the division $5 \div 9$. The result is approximately $0.56$.
Next, add this decimal result to the integer part of the mixed number. In this example, add $1$ to $0.56$, resulting in $1.56$.

Understanding this conversion is crucial for many applications, such as preparing data for further mathematical operations and solving real-world problems.

Decimal Conversion

Decimals are a standardized way of expressing numbers that aren't whole, and they are particularly useful for expressing fractional values in a form more accessible for various calculations.

Once a mixed number is converted to a decimal, as we did with $1 \frac{5}{9} = 1.56$, you can perform further transformations, like converting it to a percentage.
Decimals represent parts of a whole and simplify operations such as addition, subtraction, multiplication, and division.
Decimals are essential for converting values into percentages because they provide a clear path for scaling a number by 100, which is the basis for calculating percentages.

With consistent practice, transforming decimals into other forms becomes intuitive, offering a clear doorway into more complex mathematical concepts.

Fractional Form

Fractions provide an alternative method to express numbers that are not whole. They are composed of a numerator (the top number) and a denominator (the bottom number).

The fractional form $\frac{5}{9}$ represents five parts out of nine equal parts of a whole.
Converting a fraction to a decimal involves dividing the numerator by the denominator, as seen when $5 \div 9$ yields approximately $0.56$.
This decimal can then interact with the integer portion of a mixed number to assist in other conversions, such as to percentages.

Fractions are fundamental in doing precise calculations and can be converted back and forth between decimals as needed. By mastering this interconversion, solving diverse mathematical problems becomes more approachable.

Mathematical Operations

Mathematical operations are actions that change or transform numbers. Understanding these is crucial for converting between mixed numbers, decimals, and percentages.

To convert a decimal to a percent, multiply by 100. For instance, $1.56 * 100$ transforms the decimal to $156\%$.
Multiplying by 100 effectively shifts the decimal point two places to the right, making it straightforward to see the percentage equivalent.
Operations like addition and division are foundational when converting mixed numbers to decimals, such as adding $1$ to $0.56$ to get $1.56$.

By routinely practicing these operations, you can fluently navigate and compute between these formats, significantly enhancing your problem-solving toolkit.

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91影视

Write as a percent. Write the remainder in fractional form. $$1 \frac{5}{9}$$

Short Answer

Step by step solution

Convert Mixed number to Decimal

Convert Decimal to Percent

Key Concepts

Mixed Number Conversion

Decimal Conversion

Fractional Form

Mathematical Operations

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