Chapter 5: Q16. (page 224)

Write the decimal as a fraction or mixed number.
$0 . \bar{78}$

Short Answer

Expert verified

$\frac{78}{99}$ is the fraction number of decimal $0 . \bar{78}$

Step by step solution

Step 1. Given information

Consider, the decimal $0 . \bar{78}$ provided in question

Step 2. Calculation

To evaluate fraction number of decimal $0 . \bar{78}$ , it is needed to remove the bar as here two digits are repeating so multiply the number by 100

Therefore, the fraction number obtained as

$\begin{matrix} x = 0. \bar{78} \\ = 0.7878... equation (1) \end{matrix}$

By multiplying 100 each sides

$100 x = 78.7878 . . . equation (2)$

Subtract equation (1) from the equation (2).

$\begin{matrix} 100 x - x = 78.7878... - .7878... \\ 99 x = 78 \\ x = 0. \bar{78} \\ = \frac{78}{99} \end{matrix}$

Hence,

$\frac{78}{99}$ is the fraction number of decimal $0 . \bar{78}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Write the decimal as a fraction or mixed number.
$0 . \bar{78}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Geometry

Decision Maths

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Write the decimal as a fraction or mixed number.0.78¯

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Geometry

Decision Maths

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Write the decimal as a fraction or mixed number.
$0 . \bar{78}$