Percent to decimal

Here you will learn about converting percents to decimals.

Students will first learn about converting percents to decimals 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 percent to decimal?

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

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

For example,

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

What is percent to decimal?

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 percentages to decimals

In order to convert from a percent to a number in its decimal form, you need to:

1. Divide the percent by $\bf{100}$.
2. Clearly state the answer showing ‘percent’ = ‘decimal’.

Percent to decimal examples

Example 1: converting a simple percentage to a decimal.

Convert $60\%$ to a decimal.

1. Divide the percent by $\bf{100}$.

You know that the percent sign $(\%)$ means the number is out of $100.$

Therefore, if you divide the number (without the percent symbol) by one hundred, you will have the equivalent decimal without having changed its value.

$60\% = 60\div100=0.6$

If you are not sure how to divide a number by $100,$ review place value and/or dividing by powers of $10.$ A summary of the process is below for this example.

When you divide by $100,$ you move the digits two places to the right. The decimal point does not move.

Here you can see that the $6$ has moved from the tens place to the tenths place in the first decimal place.

You can see that the $0$ has moved from the ones place to the hundredths place in the second decimal place.

Therefore,

$60\div100=0.60=0.6$

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

$60\% = 0.6$

Example 2: converting a percentage to a decimal

Convert $8\%$ to a decimal.

Example 3: converting a percentage (involving a decimal) to a decimal

Convert $52.3\%$ to a decimal.

Example 4: converting a percentage (involving a repeating decimal) to a decimal

Convert $4.\overline{2}\%$ to a decimal.

Example 5: converting a percentage (above 100) to a decimal

Convert $145.1\%$ to a decimal.

Example 6: converting a percentage to a decimal

Convert $102.04\%$ to a decimal.

Teaching tips for percent to decimal

• Use visual models such as hundreds grids or pie charts to illustrate the equivalence of percents and decimals 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 percentages can be thought of as decimals.

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

Easy mistakes to make

• Dividing incorrectly by $\bf{100}$
  Often mistakes are made when dividing by $100.$ The common mistakes are:
  ◌ Dividing by $10$ instead of $100.$
  ◌ Multiplying instead of dividing.
  ◌ Mistakes with decimals.
  Make sure you are confident with the below equations:
  Example,
  $4 \div 100=0.04$
  $0.4 \div 100=0.004$
  $0.04 \div 100=0.0004$

• Not including repeating decimals in the percentages
  You need to remember to take the repeating decimal into account when dividing by a power of $10.$
  Example,
  $0.\overline{4} \div 10=0.0\overline{4}$ not $0.04$

Related lessons on converting fractions, decimals, and percentages

• Fraction to percent
• Percent to fraction
• Decimal to percent
• Decimal to fraction
• Fraction to decimal
• Repeating decimal to fraction

The next lessons are

• Percent
• Compound measures
• Arithmetic
• Properties of equality
• Decimals

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