**Fractions and Decimals**

## Lesson 7 Conversions of Decimals

**Welcome Friends!!**In this lesson we will learn the conversions of Decimals to Vulgar Fractions and vice a versa.**Objectives:**Convert Vulgar Fractions to Decimal.

And Convert Decimal to Vulgar Fractions

**Vulgar Fractions:**The numbers with numerator and denominator is called ‘Vulgar Fraction’ e.g. 7/5, ¾ 2/9 etc.

Decimal numbers have a decimal point in them. e.g. 2.33, 12.56 etc.**Conversion:****Vulgar Fraction to Decimal.**

We will explain the conversion using different examples.

1. Let us consider a vulgar fraction 37/10. Since the denominator is 10, that is it has one zero in it. The fraction will have only one decimal place. We start counting from right while inserting the decimal point.

37/10 = 3.7

2. You have 37/1000, how would you represent it in the decimal form?

The denominator is 1000, so we will move three places from right of 37 to place a decimal point.

So the decimal form of 37/1000 is 0.037

3. Write 1 ½ as Decimal.

· Step 1.

o Look at the fraction part

o The denominator 2 is not a power of ten. Write an equivalent fraction with a denominator that is power of ten.

o 2* 5 = 10

o So multiply the numerator and denominator by 5. ½ = 5/10

· Step 2:

o The whole number part is 1, so write 1 then write the decimal pint.

· Step 3:

o The denominator is 10, so the decimal ends in the tenths place.

· Step 4:

o Write the numerator 5, in the tenth place.

o So 1 ½ = 1.5

4. Write 1/8 as a decimal.

o Step 1 :

§ You can write a fractions as a decimal by deviding numerator by denominator 1/8 ,

§ Write this using the long division symbol.

o Step 2

§ Divide the same way you would divide the whole number, but place a decimal point in the answer first. And perform the division.

§ The answer is 1/8 = 0.125

**Converting a Decimal into a Vulgar Fraction.**

Let us consider a decimal 15.71

· In this we know that 15 is an integer and have two places after decimal point.

· So 0.71 will be written as 71/100

· Hence number 15.71 will be represented as 15 71/100

## Practice Problems

Practice Problems:Remember you will simply solve these problems on your own; It is

Convert following decimals to vulgar fractions

1. 12.56

2. 23.778

3. 45. 890

Convert following fractions to decimals.

1. 2/5

2. 2 1/8

**not**needed to email the answers to the instructor.Convert following decimals to vulgar fractions

1. 12.56

2. 23.778

3. 45. 890

Convert following fractions to decimals.

1. 2/5

2. 2 1/8

## Assignment 7

**Please email the answers to this Assignment 7 to the email address provided at the bottom of the page. Do not forget to write the Assignment number.**

Convert following Decimal numbers to vulgar fractions

1. 1.3

2. 0.4

3. 0.005

4. 4.35

5. 2.65

Convert following vulgar fractions to Decimals.

1. 4/10

2. 34/100

3. 27/1000

4. 8/11

5. 1 3/8

## Assessment 7

**Please email the answers to this Assessment 7 to the email address provided at the bottom of the page. Do not forget to write the Assessment number.**

Convert following Decimal numbers to vulgar fractions

1. 3.3

2. 2.5

3. 33.005

4. 4.12

5. 3.66

Convert following vulgar fractions to Decimals.

1. 5/10

2. 299/100

3. 127/1000

4. 7/17

5. 2 5/9

## Objectives of next lesson

Brief Objective of next Lesson: In the next lesson we will study Mathematical Operations on Decimals

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**Please email your assignments and assessments to: dskarkha@ncsu.edu**.