/*! 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 25 Find decimal notation. \(\frac... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 25

Find decimal notation. \(\frac{4}{15}\)

Short Answer

Expert verified
0.266\(\bar{6}\)

Step by step solution

01

Understand the Problem

The task is to convert the fraction \(\frac{4}{15}\) into decimal notation.
02

Divide the Numerator by the Denominator

Perform the division \(\frac{4}{15}\) by dividing 4 (the numerator) by 15 (the denominator) using long division.
03

Perform the Division

When 4 is divided by 15, the result is approximately 0.2666, which is a repeating decimal. Therefore, \(\frac{4}{15}\) can be written as 0.2666...
04

Write the Repeating Decimal in Notation

The repeating part of the decimal 0.2666 can be written with a bar over the repeated digits: 0.266\(\bar{6}\).

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Key Concepts

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

Fraction to Decimal Conversion
Converting a fraction to decimal notation is a common task in mathematics. A fraction represents a division between two numbers. For example, \(\frac{4}{15}\) means you are dividing 4 by 15. This operation will yield a decimal result. To perform this conversion:
  • Identify the numerator (the top number) and the denominator (the bottom number).
  • Use division to convert the fraction into a decimal.
In our example, \(\frac{4}{15}\) can be converted to decimal by dividing 4 by 15. This process can be done manually using long division or with a calculator.
Repeating Decimal
A repeating decimal is a decimal fraction in which a sequence of digits repeats infinitely. These are also known as recurring decimals. For example, when you convert the fraction \(\frac{4}{15}\) to a decimal, you get 0.2666..., where the digit 6 repeats indefinitely. To represent a repeating decimal:
  • Identify the repeating digit or group of digits.
  • Place a bar over the repeating digit(s).
For \(\frac{4}{15}\), this means writing it as 0.266\(\text{{\textasciimacron}}6\), indicating that only the digit 6 repeats.
Long Division
Long division is a method used to convert fractions to decimals. This method is helpful when you need to see the decimal form of a fraction. Here are the steps to perform long division for \(\frac{4}{15}\):
  • Set up the division problem with 4 (the numerator) as the dividend and 15 (the denominator) as the divisor.
  • Estimate how many times 15 can go into the numerator. In this case, 15 cannot divide into 4, so we use 0 initially.
  • Add a decimal point and zeros to the right of 4, making it 40, 400, etc.
  • Continue the division process, bringing down each zero and finding how many times 15 fits into the new number.
  • Record each answer as a digit in the resulting decimal.
When you do this for 4 divided by 15, you will get an approximate answer of 0.2666..., confirming the repeating nature of the decimal.

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