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Chapter 2: Problem 4

Write each decimal as a mixed number. 7.016

Short Answer

Expert verified
7 \( \frac{2}{125} \)

Step by step solution

01

- Identify the Whole Number

Separate the whole number part from the decimal part. For 7.016, the whole number part is 7.
02

- Convert the Decimal Part to a Fraction

The decimal part is 0.016. To convert this to a fraction, recognize that 0.016 means 16 thousandths, which can be written as \( \frac{16}{1000} \).
03

- Simplify the Fraction

Simplify \( \frac{16}{1000} \) by finding the greatest common divisor (GCD). The GCD of 16 and 1000 is 8. So, \( \frac{16}{1000} = \frac{16 \div 8}{1000 \div 8} = \frac{2}{125} \).
04

- Write as a Mixed Number

Combine the whole number and the simplified fraction. The mixed number is 7 \( \frac{2}{125} \).

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Key Concepts

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

Mixed Numbers
A mixed number is a combination of a whole number and a fraction. For example, 7.016 can be written as a mixed number because it has both a whole number part (7) and a decimal part (0.016). To convert a decimal to a mixed number, first identify the whole number part and then convert the decimal part into a fraction. Finally, simplify the fraction if possible and combine it with the whole number.
Fraction Simplification
Fraction simplification involves reducing a fraction to its simplest form. For instance, when converting 0.016 to a fraction, we get 16/1000. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 16 and 1000 is 8. Simplifying the fraction, we get:\[ \frac{16}{1000} = \frac{16 \div 8}{1000 \div 8} = \frac{2}{125} \]Simplifying fractions makes calculations easier and the result more understandable.
Greatest Common Divisor (GCD)
The greatest common divisor (GCD) is the largest positive integer that divides two or more integers without leaving a remainder. For example, to simplify the fraction 16/1000, we need to find the GCD of 16 and 1000. Steps to find the GCD include:
  • List the factors of each number.
  • Identify the common factors.
  • Select the largest common factor.
For 16, the factors are: 1, 2, 4, 8, 16.For 1000, the factors are: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000.The common factors are 1, 2, 4, 8.Thus, the GCD of 16 and 1000 is 8.Finding the GCD is crucial for simplifying fractions and making mathematical expressions easier to handle.

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