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Chapter 6: Problem 20

Convert each decimal fraction to a proper fraction or a mixed number. Be sure to reduce. 1.355

Short Answer

Expert verified
1.355 is the mixed number \( 1\frac{71}{200} \).

Step by step solution

01

Identify the Whole Number Part

Look at the number given, which is 1.355. Identify the whole number part, which in this case is 1.
02

Convert the Decimal to a Fraction

Take the decimal part 0.355 and convert it into a fraction. The fraction form of 0.355 is \( \frac{355}{1000} \) since there are three decimal places.
03

Simplify the Fraction

To simplify \( \frac{355}{1000} \), find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 355 and 1000 is 5. Divide both the numerator and the denominator by 5 to get \( \frac{71}{200} \).
04

Write the Number as a Mixed Number

Combine the whole number part identified in Step 1 with the simplified fraction obtained in Step 3. So, the mixed number representation of 1.355 is \( 1\frac{71}{200} \).

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Key Concepts

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

Mixed Numbers
Mixed numbers are a way to express numbers that have both a whole number part and a fractional part. They are particularly useful when dealing with decimals that are greater than one, as they help to clearly separate the whole number from the fraction. For example, with the decimal 1.355, the whole number is 1. What remains is the decimal part, which can be converted into a fraction. When combining these parts, we write it as a mixed number: \(1\frac{71}{200}\). This notation simplifies reading and understanding numbers in practical use, like dealing with measurements in cooking or construction, where mixed numbers often appear.
Simplifying Fractions
Simplifying fractions is the process of making a fraction simpler by ensuring both the numerator and the denominator are as small as possible while still retaining the same value. This is done by dividing both the numerator and denominator by their greatest common divisor (GCD). For the fraction \(\frac{355}{1000}\) derived from the decimal 0.355, we simplified it by dividing both parts by 5, which is their GCD. This results in the simpler fraction \(\frac{71}{200}\). A simplified fraction is easier to interpret and can be essential for accurate calculations in various mathematical operations.
Greatest Common Divisor (GCD)
The greatest common divisor is the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder. Identifying the GCD is a crucial step in simplifying fractions. In the case of converting the decimal fraction \(\frac{355}{1000}\), we first found the GCD to be 5.
  • Calculate the GCD by listing the factors of both numbers and selecting the largest one they have in common.
  • This ensures that the fraction is reduced to its simplest form by dividing the numerator and the denominator by the GCD.
Simplifying using the GCD makes numbers more manageable and often gives a clearer representation of proportions, which can be especially helpful in real-world scenarios such as financial mathematics or statistical analysis.

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Most popular questions from this chapter

Perform each operation and simplify. \(1.2 \cdot 8.6\)

Perform each operation. $$ 15.026+5.971 $$

Perform each operation and simplify. $$ 150.79 \div 100 $$

Read each decimal by writing it in words. 8.105

Convert each fraction to a decimal. $$ 125.125 \frac{1}{8} $$
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