How to Using Decimals, Grid Models, and Fractions to Represent Percent

How to using decimals, grid models, and fractions to represent percent, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

Percentages, fractions, and decimals are three different ways to express the same part-of-a-whole idea. A \(\color{blue}{10 \times 10}\) grid (100 squares) is the classic visual tool for showing all three at once. Once you can move fluently between these representations, GED percent problems become much easier to interpret and solve.

What Are the Three Representations of Percent?

Any percentage can be written in three equivalent forms:

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• Percent: uses the % symbol (e.g., 45%)
• Decimal: divide the percent by 100 (e.g., 0.45)
• Fraction: write over 100 and simplify (e.g., \(\color{blue}{\frac{9}{20}}\))

A grid model uses a \(\color{blue}{10 \times 10}\) square (100 equal cells). Each shaded cell represents 1%.

How to Use Decimal, Grid Model, and Fraction Representations

Reading a grid model

Count the shaded squares. That count is the percent. If 45 squares are shaded, the percent is 45%, the decimal is 0.45, and the fraction is \(\color{blue}{\frac{45}{100} = \frac{9}{20}}\).

Converting percent to decimal and fraction

Divide the percent by 100 for the decimal. Write it over 100 and simplify for the fraction.

• \(\color{blue}{0.45 = 45\% = \frac{45}{100} = \frac{9}{20}}\)
• \(\color{blue}{\frac{3}{5} = 0.60 = 60\%}\) (3 ÷ \(\color{blue}{5 = 0.6}\), \(\color{blue}{\text{ then } \times 100}\))
• \(\color{blue}{7}\) shaded squares out of 100 = \(\color{blue}{7\% = 0.07 = \frac{7}{100}}\)

Converting a fraction to grid/decimal/percent

Divide numerator by denominator to get the decimal, then multiply by 100 to get the percent. Shade that many squares on a \(\color{blue}{10 \times 10}\) grid.

Step-by-Step Summary

1. Start from whichever form you have (percent, decimal, or fraction).
2. To get the decimal: percent ÷ 100, OR fraction: numerator ÷ denominator.
3. To get the percent: \(\color{blue}{\text{ decimal } \times 100}\).
4. To get the fraction: write \(\color{blue}{\frac{\text{ percent }}{100}}\) and simplify (or convert decimal to fraction).
5. On a grid: shade (percent value) squares out of 100.

Watch: Percents and Equivalent Fractions (Video Lesson)

Math Antics shows how percents and fractions are equivalent, the foundation of grid-model thinking:

Worked Examples

Example 1: A \(\color{blue}{10 \times 10}\) grid has 45 shaded squares. Express as a percent, decimal, and fraction.

Percent: \(\color{blue}{45\%}\). Decimal: \(\color{blue}{45 &\text{ div }; 100 = 0.45}\). Fraction: \(\color{blue}{\frac{45}{100} = \frac{9}{20}}\).
Answer: 45%, 0.45, \(\color{blue}{\frac{9}{20}}\)

Example 2: Express \(\color{blue}{\frac{3}{5}}\) as a percent and a decimal.

\(\color{blue}{3 &\text{ div }; 5 = 0.60}\). Percent: \(\color{blue}{0.60 \times 100 = 60\%}\).
Answer: 60%, 0.60

Example 3: 7 cells in a 100-square grid are shaded. Write as a decimal and fraction.

Decimal: \(\color{blue}{0.07}\). Fraction: \(\color{blue}{\frac{7}{100}}\) (already in simplest form).
Answer: 0.07, \(\color{blue}{\frac{7}{100}}\)

Example 4: Express 0.04 as a percent and as a fraction.

Percent: \(\color{blue}{0.04 \times 100 = 4\%}\). Fraction: \(\color{blue}{\frac{4}{100} = \frac{1}{25}}\).
Answer: 4%, \(\color{blue}{\frac{1}{25}}\)

More Practice: Converting Fractions, Decimals, and Percents

Math with Mr. J walks through all conversions in a comprehensive mini-course:

Exercises

1. A grid has 72 shaded squares out of 100. Write as a percent, decimal, and simplified fraction.
2. Express \(\color{blue}{\frac{2}{5}}\) as a percent and decimal.
3. Convert 0.125 to a percent and fraction in simplest form.
4. Write 15% as a decimal and fraction.
5. How many squares should be shaded on a 100-grid to represent 8%?

Answers

1. \(\color{blue}{72\%, 0.72, \frac{18}{25}}\)
2. \(\color{blue}{40\%, 0.40}\)
3. \(\color{blue}{12.5\%, \frac{1}{8}}\)
4. \(\color{blue}{0.15, \frac{3}{20}}\)
5. \(\color{blue}{8 \text{ squares }}\)

Frequently Asked Questions

What do fractions, decimals and percents have in common?

Fractions, decimals and percents are three ways of writing the same part of a whole. For example, 9/20, 0.45 and 45% all describe the same amount. On a 10 × 10 grid of 100 squares, all three would show 45 shaded squares. Choosing the form that fits a problem best, such as percent for discounts or decimals for calculator work, makes many GED questions quicker to solve.

How do you convert a percent to a fraction and a decimal?

To get the decimal, divide the percent by 100, which moves the decimal point two places left: 35% becomes 0.35. To get the fraction, write the percent over 100 and simplify: 35/100 = 7/20. A grid model helps you check, since 35 shaded squares out of 100 show the same value in all three forms.

How do you turn fractions into decimals and percents?

Divide the numerator by the denominator to get the decimal, then multiply by 100 to get the percent. For 3/5, 3 ÷ 5 = 0.6, and 0.6 × 100 = 60%. If the denominator divides evenly into 100, you can also rewrite the fraction over 100 first: 3/5 = 60/100, which is 60 shaded squares on a hundred grid.

How do you compare fractions, decimals and percentages?

Convert all the values to the same form, usually decimals, and then compare them. To compare 2/5, 0.38 and 41%, rewrite them as 0.40, 0.38 and 0.41. Now it is clear that 41% is the largest and 0.38 is the smallest. Shading each value on its own hundred grid is another quick visual check.

How do you order fractions, decimals and percentages?

Change every number to a decimal, line them up by place value, and then list them from least to greatest or greatest to least. For example, 7/20 = 0.35, 0.3 stays 0.3, and 32% = 0.32, so the order from least to greatest is 0.3, 32%, 7/20. Write the final answer using the original forms.

Is there a fractions, decimals and percents chart?

Yes, a conversion chart lists common values side by side so you can learn them quickly. Useful pairs to memorize include 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/10 = 0.1 = 10% and 1/8 = 0.125 = 12.5%. Knowing these by heart saves time on GED percent problems.

Related Topics

• Representing Percentage
• Using Grid Models to Solve Percentage Problems
• Fractional and Decimal Percentages
• Convert Between Fractions and Decimals
• Word Problems of Percent Fractions Decimals