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Chapter 4: Problem 12

Find decimal notation. \(\frac{7}{8}\)

Short Answer

Expert verified
0.875

Step by step solution

01

Understand the Problem

The goal is to convert the fraction \( \frac{7}{8} \) into its decimal notation. This can be achieved through division.
02

Set Up the Division

Set up the fraction 7 divided by 8. This means you will divide 7 by 8.
03

Perform the Division

Perform the division \( 7 \, 梅 \, 8 \). When you divide 7 by 8, it equals 0.875.

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Key Concepts

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

Understanding Fractions
Fractions represent a part of a whole. They are written as two numbers separated by a slash. The number on the top is called the numerator. The number on the bottom is called the denominator.
In the fraction \(\frac{7}{8}\), the 7 is the numerator and the 8 is the denominator.
The numerator tells you how many parts you have. The denominator tells you how many equal parts the whole is divided into.
  • In \(\frac{7}{8}\), imagine something divided into 8 equal parts.
  • We have 7 of these parts.
This means \(\frac{7}{8}\) is slightly less than one whole part, since 7 out of 8 parts are included.
Performing Division
Converting a fraction to a decimal often involves division. The fraction \(\frac{7}{8}\) means we divide 7 by 8.
Division is the process of determining how many times one number is contained within another. It's often more intuitive with smaller numbers or when using a calculator.
When dividing 7 by 8, think about how many times 8 fits into 7. Since 8 is larger than 7, it doesn't fit even once, indicating a result less than 1.
To divide 7 by 8 (or any smaller numerator by a larger denominator), you can use long division:
  • Place 7 under the division bar and 8 outside.
  • You realize 8 cannot go into 7 even once, so the first digit in our quotient is 0.
  • Add a decimal point and bring down a 0 to make it 70. Now consider how many times 8 fits into 70.
Continuing this process eventually gives you 0.875, which is the decimal notation for \(\frac{7}{8}\).
Decimal Notation
Decimal notation is a way of expressing numbers that are not whole. It uses a decimal point to separate the whole part from the fractional part.
For example, in the number 0.875, the digit before the decimal point represents units. The digits after the decimal point represent parts of one:
  • The first digit after the decimal is tenths.
  • The second digit is hundredths.
  • The third digit is thousandths.
In \(\frac{7}{8}\) = 0.875, 8 goes into 7 with a result of 0.875, meaning 7 is less than a full 8, but takes up 875 thousandths of it.
Understanding how to read and use decimal notation is important for various mathematical and real-life applications, such as measuring and handling money.

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Most popular questions from this chapter

The following were done on a calculator. Estimate to determine whether the decimal point was placed correctly. $$ 28.46901 \div 4.9187-2.5081=3.279813473 $$

Subtract. $$ 34.07-30.7 $$

Estimate. Indicate which of the choices is an appropriate estimate. \(49 \times 7.89\) a) 400 b) 40 c) 4 d) 0.4

Estimate. Indicate which of the choices is an appropriate estimate. \(3.6 \div 4\) a) 10 b) 1 c) 0.1 d) 0.01

Add. $$ 0.34+3.5+0.127+768 $$
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