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Chapter 1: Problem 617

Convert each fraction to a decimal. $$ \frac{17}{20} $$

Short Answer

Expert verified
0.85

Step by step solution

01

- Understand the Fraction

The given fraction is \(\frac{17}{20}\). This fraction represents the division of 17 by 20.
02

- Perform the Division

Divide 17 by 20 using long division or a calculator. When you divide 17 by 20, you get 0.85.

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Key Concepts

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

Division
Division is a basic mathematical operation where a number (called the dividend) is divided by another number (called the divisor) to find out how many times the divisor fits into the dividend. In our problem, 17 is the dividend, and 20 is the divisor. When we are converting a fraction like \( \frac{17}{20} \) to a decimal, we need to divide the numerator (17) by the denominator (20). This isn't always straightforward without understanding the steps involved. Using division allows us to convert fractions into a format that's often easier to understand.
Long Division
Long division is a method used to divide larger numbers that cannot be easily divided mentally. For \( \frac{17}{20} \), we need to divide 17 by 20. Let's break it down step by step:
  • First, because 17 is smaller than 20, we add a decimal point and a zero to the right of 17, making it 170.
  • We then see how many times 20 fits into 170, which is 8 times (since 20 * 8 = 160).
  • Write down 8 in the quotient (the answer area), and subtract 160 from 170, leaving a remainder of 10.
  • Next, bring down another 0, making it 100. Then, determine how many times 20 can fit into 100, which is 5 times (since 20 * 5 = 100).
  • Write down 5 in the quotient, and subtract 100 from 100, resulting in 0, which means we're done.
The quotient we've written down step by step is 0.85, which is our decimal representation of \( \frac{17}{20} \).
Decimal Representation
Decimal representation is when a number is expressed in a system based on powers of 10. For example, the fraction \( \frac{17}{20} \) converted into decimal form is 0.85. Here, the digit to the left of the decimal, 0, represents the ones place, and the digits to the right represent tenths and hundredths places (8 tenths and 5 hundredths in this case). This format can make it easier to understand and compare sizes of different numbers. Decimals are commonly used in everyday life, particularly with money, measurements, and precise calculations.

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Most popular questions from this chapter

Insurance copayment Carrie had to have 5 fillings done. Each filling cost $$\$ 80\(. Her dental insurance required her to pay \)20 \%\( of the cost as a copay. Calculate Carrie's copay: (a) First, by multiplying 0.20 by 80 to find her copay for each filling and then multiplying your answer by 5 to find her total copay for 5 fillings. (b) Next, by multiplying \)[5(0.20)](80)\( (c) Which of the properties of real numbers says that your answers to parts (a), where you multiplied \)5[(0.20)(80)]\( and \)(b),\( where you multiplied \)[5(0.20)](80),$$ should be equal?

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