# Converting Fractions to Decimals

#### Grade 7 Math Worksheets

**To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number) using long division or a calculator.**

Table of Contents:

- Converting Fractions to Decimals
- Formula
- Solved Examples
- FAQs

**Personalized Online Tutoring**

## Converting Fractions to Decimals - Grade 7 Math Worksheet PDF

This is a free worksheet with practice problems and answers. You can also work on it online.

Sign up with your email ID to access this free worksheet.

### "We really love eTutorWorld!"

*"We really love etutorworld!. **Anand S and Pooja are excellent math teachers and are quick to respond with requests to tutor on any math topic!" - Kieran Y (via TrustSpot.io)*

### "My daughter gets distracted easily"

*"My daughter gets distracted very easily and Ms. Medini and other teachers were patient with her and redirected her back to the courses.*

* With the help of Etutorworld, my daughter has been now selected in *

*the*

**Gifted and Talented Program**for the school district"*- Nivea Sharma (via TrustSpot.io)*

## Converting Fractions to Decimals

To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number) using long division or a calculator.

Here’s an example:

Convert 3/4 to a decimal.

Solution:

Divide 3 by 4: 0 .75

____

4 | 3.00

– 0

—

3

The quotient is 0.75, so 3/4 is equal to 0.75 as a decimal.

**Another example:**

Convert 5/8 to a decimal.

Solution:

Divide 5 by 8:

0 .625

_____

8 | 5.000

– 4.0

—-

1.00

– .8

—

20

The quotient is 0.625, so 5/8 is equal to 0.625 as a decimal.

Note that sometimes the division will result in a repeating decimal, such as when converting 1/3 to a decimal (which is 0.3333…). In these cases, it may be necessary to round the decimal to a certain number of decimal places, depending on the desired level of precision.

## Formula

The formula to convert a fraction to a decimal is:

**Decimal = Numerator / Denominator**

For example, if you want to convert the fraction 3/4 to a decimal, you would divide 3 by 4:

Decimal = 3 / 4 = 0.75

If the fraction has a repeating decimal, you can use the following formula to represent it:

Fraction = Whole number + (Repeating decimal / (10^n – 1))

For example, the fraction 1/3 can be represented as:

1/3 = 0.3333… = 0 + (0.3 / (10^1 – 1))

Where the repeating decimal 0.3 is divided by 10^1 – 1 = 9 to get 0.3/9 = 0.03. So, 1/3 can be represented as:

1/3 = 0.3(Repeating) = 0 + 0.03/9

Note that this formula works only for repeating decimals that have one digit repeating. For more complicated repeating decimals, other methods may be necessary.

*“**There have been times when we booked them last minute, but the teachers have been extremely well-prepared and the help desk at etutorworld is very prompt. *

*Our kid is doing much better with a higher score.**”*

### 7th Grade Tutoring

eTutorWorld offers **Personalized Online Tutoring** for Math, Science, English, and Standardised Tests.

Our Tutoring Packs start at just under** $21 per hour**, and come with a moneyback guarantee.

**Schedule a FREE Trial Session**, and experience quality tutoring for yourself. (No credit card required.)

## Solved Examples

Sure! Here are some examples of converting fractions to decimals:

**Example 1: Convert 2/5 to a decimal**

To convert 2/5 to a decimal, divide the numerator (2) by the denominator (5):

2 ÷ 5 = 0.4

Therefore, 2/5 is equal to 0.4 as a decimal.

**Example 2: Convert 3/8 to a decimal**

To convert 3/8 to a decimal, divide the numerator (3) by the denominator (8):

3 ÷ 8 = 0.375

Therefore, 3/8 is equal to 0.375 as a decimal.

**Example 3: Convert 7/12 to a decimal**

To convert 7/12 to a decimal, divide the numerator (7) by the denominator (12):

7 ÷ 12 = 0.5833…

Since the decimal repeats, we can either round to a certain number of decimal places or use the formula for a repeating decimal. Let’s round to two decimal places:

7/12 = 0.58 (rounded to two decimal places)

**Example 4: Convert 5/6 to a decimal**

To convert 5/6 to a decimal, divide the numerator (5) by the denominator (6):

5 ÷ 6 = 0.8333…

Since the decimal repeats, we can use the formula for a repeating decimal:

5/6 = 0.83(Repeating) = 0 + 0.03/9

Therefore, 5/6 is equal to 0.83(Repeating) or 0.8333…

### Do You Stack Up Against the Best?

If you have 30 minutes, try our free diagnostics test and assess your skills.

## Converting Fractions to Decimals FAQS

##### What does it mean to convert a fraction to a decimal?

Converting a fraction to a decimal means expressing a fraction as a decimal number, typically with a decimal point and decimal places.

##### How do I convert a fraction to a decimal?

To convert a fraction to a decimal, divide the numerator (the top number) of the fraction by the denominator (the bottom number).

##### Can all fractions be converted to decimals?

Yes, all fractions can be converted to decimals. However, the resulting decimal may be a terminating decimal (a decimal with a finite number of digits) or a repeating decimal (a decimal with a recurring pattern of digits).

##### What is a terminating decimal?

A terminating decimal is a decimal that ends after a finite number of digits. For example, 0.5, 0.75, and 0.125 are examples of terminating decimals.

##### What is a repeating decimal?

A repeating decimal is a decimal that has a repeating pattern of digits. The repeating pattern is indicated by placing a line or bar over the repeating digits. For example, 0.333… and 0.714285714285… are examples of repeating decimals.

**Gloria Mathew** writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

### Affordable Tutoring Now Starts at Just $21

eTutorWorld offers affordable one-on-one live tutoring over the web for Grades K-12. We are also a leading provider of Test Prep help for Standardized Tests (SCAT, CogAT, MAP, SSAT, SAT, ACT, ISEE, and AP).

What makes eTutorWorld stand apart are: flexibility in lesson scheduling, quality of hand-picked tutors, assignment of tutors based on academic counseling and diagnostic tests of each student, and our 100% money-back guarantee.

Whether you have never tried personalized online tutoring before or are looking for better tutors and flexibility at an affordable price point, schedule a **FREE TRIAL **Session with us today.

**There is no purchase obligation or credit card requirement*

## Grade 7 Science Worksheets

- Elements and Compounds
- Solar Energy
- Photosynthesis
- Electricity and Magnetism
- Law of conservation of energy
- Periodic table
- Properties of Matter
- Waves
- Energy Resources
- Weather and Climate
- Immune, Circulatory and Digestive Systems
- Organs in Multi-cellular Organism
- Sedimentary, Igneous, and Metamorphic Rocks
- Structure of the Earth
- Law of Conservation of Mass
- Physical and Chemical Changes
- Scientific Method
- Human Digestive System
- Environmental Science
- Renewable and Non-renewable energy Resources
- Characteristics of Living Organisms
- Life Science
- Earth and Space Science
- Solar Eclipse
- Heat Technology
- Newton’s Laws of Motions
- Physical Science
- Tools, Measurement and SI Units
- Earth Atmosphere
- Interactions of Living things
- The Earth Ecosystem
- Organelles in Plant and Animal cells
- Layers of the Earth
- Cycles in Nature

## Grade 7 Math Worksheets

- Fractions
- Linear equations word problems
- Statistics
- Properties of Parallel Line
- Finding slope from an equation
- Identifying Quadrilaterals
- Percent Change
- Properties of addition and multiplication
- Pythagorean Theorem
- Solving two step inequalities
- Symmetry
- Fractions to Decimals (New)
- Whole Number Exponents with Integer Bases (New)
- Adding and Subtracting Fractions (New)
- Integer Addition and Subtraction (New)
- Dividing Mixed Numbers (New)
- Basics of Coordinate Geometry (New)

## IN THE NEWS

Our mission is to provide high quality online tutoring services, using state of the art Internet technology, to school students worldwide.

**Online test prep and practice**

SCAT

CogAT

SSAT

ISEE

PSAT

SAT

ACT

AP Exam

**Science Tutoring**

Physics Tutoring

Chemistry Tutoring

Biology Tutoring

**Math Tutoring**

Pre-Algebra Tutoring

Algebra Tutoring

Pre Calculus Tutoring

Calculus Tutoring

Geometry Tutoring

Trigonometry Tutoring

Statistics Tutoring

**Quick links**

Free Worksheets

Fact sheet

Sales Partner Opportunities

Parents

Passive Fundraising

Virtual Fundraising

Our Expert Tutors

Safe and Secure Tutoring

Interactive Online Tutoring

After School Tutoring

Elementary School Tutoring

Middle School Tutoring

High School Tutoring

Home Work Help

Math Tutors New York City

Press

©2022 eTutorWorld Terms of use Privacy Policy Site by Little Red Bird

©2022 eTutorWorld

Terms of use

Privacy Policy

Site by Little Red Bird