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

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. \(\color{blue}{8 \text{ squares }}\)

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Frequently Asked Questions

Why is a \(\color{blue}{10 \times 10}\) grid used to model percentages?

A \(\color{blue}{10 \times 10}\) grid has exactly 100 cells, making each cell worth exactly 1%. This makes it easy to read off a percent by simply counting shaded cells, and to convert to a fraction by writing the count over 100.

What if the fraction doesn’t convert to a whole percent?

Some fractions produce repeating decimals (e.g., \(\color{blue}{\frac{1}{3} = 0.333}\)… = 33.3%). On a grid you would shade approximately 33 full cells (and a partial cell). In calculations, keep the exact decimal or fraction form.

Is 0.5 the same as 50%?

Yes. \(\color{blue}{0.5 \times 100 = 50\%}\), and on a 100-grid, 50 cells would be shaded. All three forms — 0.5, 50%, and \(\color{blue}{\frac{1}{2}}\) — are equivalent.

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