Math Problem Statement

show full steps and calculation of 4.4

Solution

To understand what you're asking for with "4.4," I will assume you're asking for an explanation or breakdown of the decimal value 4.4 in various forms (like as a fraction, its properties, etc.). I'll show different ways to represent and work with this number.

Step-by-step breakdown of 4.4:

1. Converting 4.4 to a fraction:

The number 4.4 is a decimal number. To convert it to a fraction:

  • 4.4 can be written as 4.4=44104.4 = \frac{44}{10}.
  • To simplify, divide both the numerator and denominator by their greatest common divisor (GCD), which is 2:

4410=225\frac{44}{10} = \frac{22}{5}

Thus, 4.4 as a fraction is 225\frac{22}{5}.

2. Converting 4.4 to a mixed number:

Since 225\frac{22}{5} is an improper fraction (numerator is larger than the denominator), you can convert it to a mixed number:

  • Divide 22 by 5, which gives a quotient of 4 and a remainder of 2.

So, 225=425\frac{22}{5} = 4 \frac{2}{5}.

Thus, 4.4 can be expressed as the mixed number 4254 \frac{2}{5}.

3. Rounding 4.4 to different places:

  • Nearest whole number: Round 4.4 to 4 (since 0.4 is less than 0.5).
  • Nearest tenth: Since it's already at one decimal place, rounding to the nearest tenth keeps it as 4.4.

4. Percentage form of 4.4:

To convert 4.4 into a percentage, multiply by 100:

4.4×100=440%4.4 \times 100 = 440\%

So, 4.4 is 440% when expressed as a percentage.

5. Scientific notation of 4.4:

The number 4.4 can be written in scientific notation as:

4.4=4.4×1004.4 = 4.4 \times 10^0

This is because the decimal point doesn't need to be moved to express it in standard form.


Summary:

  • Fraction form: 225\frac{22}{5}
  • Mixed number: 4254 \frac{2}{5}
  • Rounded: 4 (nearest whole number), 4.4 (nearest tenth)
  • Percentage: 440%
  • Scientific notation: 4.4×1004.4 \times 10^0

Do you want more details or have any questions?


Here are 5 relative questions for deeper understanding:

  1. How would you convert 4.4 to a ratio?
  2. What is the decimal representation of 225\frac{22}{5}?
  3. How would you express 4.4 as a recurring decimal?
  4. What is the square of 4.4?
  5. How would you subtract 4.4 from a whole number?

Tip: When converting a decimal to a fraction, always check if the fraction can be simplified by finding the GCD of the numerator and denominator.

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Math Problem Analysis

Mathematical Concepts

Decimals
Fractions
Mixed Numbers
Percentages
Scientific Notation

Formulas

Conversion of decimal to fraction: decimal = numerator/denominator
Simplifying fractions by dividing by the greatest common divisor (GCD)
Percentage conversion: number × 100
Scientific notation: number × 10^exponent

Theorems

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Suitable Grade Level

Grades 5-7