Chapter 5: Q55. (page 225)

Write the decimal as a fraction or mixed number.
$0 . \bar{897}$

Short Answer

Expert verified

The fraction is $\frac{299}{333}$ .

Step by step solution

Step 1. Given information

Consider, the decimal $0 . \bar{897}$ provided in question.

Step 2. Calculation

Consider $x = 0 . \bar{897}$

$x = 0 \cdot 897897897 . . . . . .$ …… (1)

Clearly, 897 is the only digit that is repeating in equation (1)

Multiply equation (1) by 1000 on both sides,

$1000 x = 897 \cdot 897897 . . . .$ …… (2)

Subtract equation (1) from equation (2),

$\begin{matrix} 1000 x - x = (897 \cdot 897897.....) - (0 \cdot 897897897......) \\ 999 x = 897 \\ x = \frac{897}{999} \end{matrix}$

Simplify further,

$\Rightarrow x = \frac{299}{333}$

Thus, the fraction number that can be formed is $\frac{299}{333}$ .

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Write the decimal as a fraction or mixed number.
$0 . \bar{897}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Write the decimal as a fraction or mixed number.0.897¯

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

Logic and Functions

Probability and Statistics

Calculus

Mechanics Maths

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Write the decimal as a fraction or mixed number.
$0 . \bar{897}$