Topics
2. Fractions, Decimals, & Percents
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United States of AmericaVirginia
Grade 6

2.03 Convert between fractions, decimals, and percents

Lesson
Practice

Convert between fractions, decimals, and percentages

We now know that decimals, fractions and percentages are just different ways of showing the same value:

1\% can be written as \dfrac{1}{100} or 1 hundredth or 0.01

Exploration

Move the slider to generate different numbers and use the checkboxes to show their equivalent fractions, decimals, and percentages.

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  1. What is the decimal and percentage equivalent of \dfrac{2}{5}?

  2. A single column of small squares is what fraction of the larger square?

  3. What do you notice when the 'Show equivalent fraction' checkbox appears?

There are some common conversions that we can remember to help us convert between percentages, fractions and decimals.

A table of benchmark fraction, decimal and percentage conversions. Ask your teacher for more information.

Examples

Example 1

Write the fraction, decimal, and percent that represents this illustration.

The image shows 4 circles divided into 8 equal parts. 27 parts are shaded.
Worked Solution
Create a strategy

First, count the number of parts in one whole circle. Then, determine how many parts are shaded. This will give the fraction. Next convert the fraction into a decimal and percent.

Apply the idea

To find the fraction:

\text{Number of parts in a whole} = 8; \text{Number of shaded parts} = 27

\text{Fraction}=\dfrac{27}{8}

To find the decimal:

\displaystyle \text{Decimal}\displaystyle =\displaystyle 27 \div 8Divide 27 by 8
\displaystyle =\displaystyle 3.375Evaluate

To find the percent:

\displaystyle \text{Percent}\displaystyle =\displaystyle 3.375 \cdot 100\%Multiply the decimal by 100\%
\displaystyle =\displaystyle 337.5\%Evaluate

Example 2

Convert between percentages, fractions and decimals to complete the table shown.

Write the answers as mixed number percentages and simplified mixed numbers where necessary.

FractionDecimalPercentage
11\%
0.83
\dfrac{5}{8}
Worked Solution
Create a strategy

To convert fractions and decimals to percentages multiply by 100\%. To convert percentages to fractions or decimals, divide by 100.

Apply the idea
\displaystyle 11\%\displaystyle =\displaystyle \dfrac{11}{100}Write as a part out of 100 (Fraction)
\displaystyle =\displaystyle 0.11Convert to a decimal
\displaystyle 0.83\displaystyle =\displaystyle 0.83 \cdot 100Multiply by 100
\displaystyle =\displaystyle 83Evaluate
\displaystyle =\displaystyle 83\%Attach percent symbol
\displaystyle =\displaystyle \dfrac{83}{100}Convert to a fraction
\displaystyle \dfrac{5}{8}\displaystyle =\displaystyle \dfrac{5\cdot 12.5}{8\cdot 12.5} Multiply by 12.5 to make the denominator equal to 100
\displaystyle =\displaystyle \dfrac{62.5}{100} Evaluate
\displaystyle =\displaystyle 62.5\%Convert to percent
\displaystyle =\displaystyle 0.625Convert to a decimal
FractionDecimalPercentage
\dfrac{11}{100}0.1111\%
\dfrac{83}{100}0.8383\%
\dfrac{5}{8}0.62562.5\%
Idea summary

Decimals, fractions and percentages can be converted between each other using the relationship:

1\%=\dfrac{1}{100}=\text{ One Hundredth }=0.01

Outcomes

6.NS.1

The student will reason and use multiple strategies to express equivalency, compare, and order numbers written as fractions, mixed numbers, decimals, and percents.

6.NS.1d

Represent and determine equivalencies among decimals, percents, fractions (proper or improper), and mixed numbers that have denominators that are 12 or less or factors of 100 incorporating the use of number lines, and concrete and pictorial models.*

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