# Decimal to percent

Here you will learn about converting a decimal to percent.

Students will first learn about converting decimals to percents in 6th grade math as part of their work with ratios and proportional relationships and will expand that knowledge to solving problems such as finding the whole given a part and the percent or finding the part given the whole and the percent.

This will later be used to find percent increase/decrease in 7th grade.

## What is decimal to percent?

Converting a decimal to percent is representing the decimal as a percentage without changing its value.

The word percent means one part out of one hundred, and you can use this information to express a decimal as a percent.

For example,

\begin{aligned} & 0.25=25 \% \\\\ & 0.45=45 \% \\\\ & 0.33333...=33.3 \% \\\\ & 0.8=80 \% \end{aligned}

## Common Core State Standards

How does this apply to 6th grade math?

• Grade 6 – Ratios and Proportional Relationships (6.RP.A.3a)
Use ratio and rate reasoning to solve real-world and mathematical problems, for example, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

## How to convert a decimal to percent

In order to convert a decimal to a percent, you need to:

1. Multiply the decimal by \bf{100} and add the percent sign ( \textbf{\%} ).
2. Clearly state the answer showing ‘decimal’ = ‘percent’.

## Decimal to percent examples

### Example 1: converting a decimal to a percent

Convert 0.7 to a percent.

1. Multiply the decimal by \bf{100} and add the percent sign ( \textbf{\%} ).

0.7\times100=70\%

The 7 has moved two places to the left. The decimal point does not move.

2Clearly state the answer showing ‘decimal’ = ‘percent’.

0.7=70\%

### Example 2: converting a decimal to a percent

Convert 0.625 to a percent.

Multiply the decimal by \bf{100} and add the percent sign ( \textbf{\%} ).

Clearly state the answer showing ‘decimal’ = ‘percent’.

### Example 3: converting a decimal to a percent (where the decimal is greater than 1)

Convert 1.23 to a percent.

Multiply the decimal by \bf{100} and add the percent sign ( \textbf{\%} ).

Clearly state the answer showing ‘decimal’ = ‘percent’.

### Example 4: converting a decimal to a percent (involving thousandths)

Convert 0.006 to a percent.

Multiply the decimal by \bf{100} and add the percent sign ( \textbf{\%} ).

Clearly state the answer showing ‘decimal’ = ‘percent’.

### Example 5: converting a repeating decimal to a percent

Convert 0.\overline{2} to a percent.

Multiply the decimal by \bf{100} and add the percent sign ( \textbf{\%} ).

Clearly state the answer showing ‘decimal’ = ‘percent’.

### Example 6: converting a repeating decimal to a percent

Convert 0.\overline{142857} to a percent.

Multiply the decimal by \bf{100} and add the percent sign ( \textbf{\%} ).

Clearly state the answer showing ‘decimal’ = ‘percent’.

### Teaching tips for decimal to percent

• Use visual models such as hundreds grids or pie charts to illustrate the equivalence of decimals to percents and to demonstrate how both forms are ways to represent a part of a whole or a rate.

• Use real world contexts to demonstrate how decimals can be thought of as percentages.

• Conversion table worksheets for decimal to percent conversion have their place, but make sure that students have a conceptual understanding of the relationship between decimals and percentages.

### Easy mistakes to make

• Mistakes with multiplication of \bf{100}
Often mistakes are made when multiplying a value by 100 by moving the digits the incorrect number of decimal places.

• Not adding a percent sign
Percents must end in a percentage symbol (\%).
For example,
50 is not a percentage but 50\% is.

• Not noticing a recurring decimal
Sometimes a repeating decimal is not immediately obvious.
For example,
\cfrac{1}{7}=0.142857142857142857...
Therefore,
\cfrac{1}{7}= 0.\overline{142857}

### Practice decimal to percent questions

1. Convert 0.1 to a percentage.

1\%

10\%

0.1\%

0.01\%

Start by multiplying the decimal value by 100.

0.1 \times 100

This gives you 10.

0.1 = 10\%

2. Convert 0.4 to a percentage.

40\%

4\%

0.4\%

40\%

Start by multiplying the decimal value by 100.

0.4 \times 100

This gives you 40.

3. Convert 1.1 to a percentage.

11\%

1.1\%

110

110\%

Start by multiplying the decimal value by 100.

1.1 \times 100

This gives you 110.

4. Convert 0.006 to a percentage.

0.6

0.06\%

6\%

0.6\%

Start by multiplying the decimal value by 100.

0.006 \times 100

This gives you 0.6.

5. Convert 30.05 to a percentage.

30.05\%

3,005\%

3,005

305\%

Start by multiplying the decimal value by 100.

30.05 \times 100

This gives you 3,005.

6. Convert 0.\overline{4} to a percentage.

44.\overline{4}\%

44\%

44.4\%

0.\overline{4}\%

Start by multiplying the decimal value by 100.

0 .\overline{4} \times 100

This gives you 44.\overline{4}.

## Decimal to percent FAQs

How do you convert a decimal to a percent?

To convert a decimal to a percent, you multiply the decimal form of the number by 100 and add the percent symbol, or percentage sign (\%).

In a repeating decimal, how many digits should be written behind the decimal point?

The repeating sequence should only be written once. If the repeating decimal value is the same digit, write one digit behind the decimal point with a line over the digit. If the repeating decimal is a sequence of three digits that repeat, write the three digits with a line over all of them.

How do I know when my answer will be greater than \bf{100}\textbf{\%} ?

If your decimal is greater than 1, your percent equivalent will be greater than 100\%.
If your decimal is less than 1, your percent equivalent will be less than 100\%.
If your decimal is equal to 1, your percent equivalent will be equal to 100\%.

## Still stuck?

At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.

Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.