/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 13 Find decimal notation. \(\frac... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 13

Find decimal notation. \(\frac{39}{40}\)

Short Answer

Expert verified
0.975

Step by step solution

01

- Understand the Fraction

The fraction given is \(\frac{39}{40}\). This is a proper fraction where the numerator (39) is less than the denominator (40).
02

- Convert the Fraction to Decimal

To convert the fraction \(\frac{39}{40}\) to a decimal, divide the numerator by the denominator. Therefore, perform the division: \ 39 \div 40. \
03

- Perform the Division

When you divide 39 by 40, you get \ 0.975 \ as the result. Therefore, \(\frac{39}{40}\) in decimal notation is \ 0.975 \.

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Key Concepts

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

Fraction to Decimal
Converting a fraction to a decimal involves changing it from its fraction form to its decimal form. It's like transforming a pie slice into a number we can easily compare with other numbers. The process is straightforward and involves division. Take the numerator, which is the top number of the fraction, and divide it by the denominator, which is the bottom number. For example, to convert \( \frac{39}{40} \) to a decimal, we simply divide 39 by 40. This division tells us how many parts of the whole (denoted by 1) the fraction represents. Hence, 39 divided by 40 equals 0.975.
Proper Fraction
A proper fraction is when the numerator (the top number) is smaller than the denominator (the bottom number). Proper fractions always represent a quantity less than 1. In our example, \( \frac{39}{40} \) is a proper fraction because 39 is less than 40. This means the fraction represents a part of a whole rather than the whole itself or more than the whole. Proper fractions are easier to visualize because they represent smaller parts of a single unit, such as one slice of a pie that has been cut into multiple pieces.
Division
Division is the core operation needed to convert a fraction to a decimal. It's a way to see how many times one number (the divisor) fits into another number (the dividend). For our conversion of \( \frac{39}{40} \) into a decimal:
  • First, set up the division problem with 39 as the dividend and 40 as the divisor.
  • Next, perform the division, which can be done manually or with a calculator.
  • Finally, the quotient, which is the result of this division, is the decimal representation of the original fraction. In this example, 39 divided by 40 gives us 0.975.
This division shows how fractional pieces fit into a whole, converting them into a decimal that is easy to use and understand.

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