Number System || Decimal to Fraction (LESSON-6)

Summary

In this lesson on converting decimal numbers into fractions, the instructor explains how to handle both simple and repeating decimals. The video distinguishes between two types of decimal representations: one with a repeating section (denoted by a bar) and one without. The instructor walks through several examples, offering step-by-step instructions on converting both types into fractions. Key concepts, such as the method of using denominators like 9, 99, or 999 depending on the number of repeating digits, are emphasized. The tutorial aims to simplify decimal-to-fraction conversion and offers helpful tips for exam preparation.

Takeaways

• 😀 The video covers converting decimal numbers into fractions, a key concept in quantitative aptitude.
• 😀 There are two types of decimal numbers: regular decimals and repeating decimals, often denoted by a bar (e.g., 0.12 bar).
• 😀 0.12 bar means 0.121212... repeating indefinitely, and this is important for understanding how to convert repeating decimals into fractions.
• 😀 To convert a simple decimal like 0.12 into a fraction, write it as 12/100, simplify it (3/25 in this case).
• 😀 The main focus of the lesson is on converting repeating decimals (model 2), which are more complex than non-repeating decimals.
• 😀 For repeating decimals, the method depends on how many digits repeat after the decimal point. One repeating digit is divided by 9, two by 99, and so on.
• 😀 Example for model 1: 0.12 (non-repeating) becomes 12/100, simplifying to 3/25.
• 😀 For model 2, where part of the decimal repeats, like 0.43 bar, the method involves subtracting the non-repeating part and dividing by the appropriate denominator (e.g., 9 for one repeating digit).
• 😀 In model 3, decimals with a non-zero integer part are handled by breaking the number into its integer and decimal parts. Each part is processed separately and then combined.
• 😀 It’s crucial to first identify whether the decimal is a simple non-repeating decimal, a repeating decimal, or a mix of both to apply the correct conversion method.

Q & A

What is the main topic of lesson number six in the video?

Lesson number six focuses on converting decimal numbers into fraction numbers, a key concept in the number system topic for quantitative aptitude.

What does the bar symbol over a decimal number signify?

The bar symbol over a decimal number indicates that the decimal repeats infinitely. For example, 0.6 bar means 0.6666..., which goes on indefinitely.

How are decimal numbers like 0.12 and 0.12 bar different when converting to fractions?

0.12 is a terminating decimal and can be directly converted into a fraction by dividing 12 by 100, whereas 0.12 bar represents a repeating decimal, which requires a specific method to convert, usually involving subtracting and dividing by 99.

How do you convert a simple decimal like 0.12 into a fraction?

To convert 0.12 into a fraction, write it as 12/100, then simplify if possible. In this case, 12/100 simplifies to 3/25.

What are the types of decimal numbers with bars, and how do they differ?

There are three types of decimal numbers with bars: Type 1 (where all decimal numbers have a bar), Type 2 (where only some decimal numbers have a bar), and Type 3 (where the number before the decimal is non-zero). Type 1 is the simplest to convert, while Type 2 and Type 3 require additional steps.

How do you handle decimals with bars in Type 2 problems?

In Type 2 problems, you handle decimals with bars by first separating the decimal into its integer and fractional parts. Then, subtract the non-barred digits from the original number and divide by 9 for one repeating digit or 99 for two repeating digits.

What is the conversion method for Type 3 decimal problems?

For Type 3 decimals, first split the number into the integer part and the repeating decimal part. Convert the repeating decimal part using Type 1 or Type 2 methods, then combine the results by cross-multiplying and simplifying.

What is the significance of the denominator in a fraction when converting from repeating decimals?

The denominator depends on how many digits repeat in the decimal. If one digit repeats, the denominator is 9; if two digits repeat, the denominator is 99; and for three repeating digits, the denominator is 999.

Can you explain how to convert a number like 0.93 bar into a fraction?

To convert 0.93 bar into a fraction, write it as 93/99, because both digits after the decimal repeat. Simplify this fraction if possible to get the final result.

How do you handle decimals with multiple non-repeating and repeating digits?

For decimals like 0.43 bar, where only one digit repeats, subtract the non-repeating part (4) from the full number (43), then divide by 9 to account for the repeating part, resulting in the fraction 39/90.