Calculate the Area: Finding the Value of One Orange Shaded Unit Square

Fraction Areas with Grid Visualization

Determine the numerical value of the shaded area:

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Determine the numerical value of the shaded area:

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the total number of divisions in the grid.
  • Step 2: Count the number of shaded divisions.
  • Step 3: Calculate the fraction of the shaded area relative to the total.

Now, let's work through each step:
Step 1: The grid is divided into 10 equal vertical columns.
Step 2: Of these columns, 1 column is shaded.
Step 3: Since there are 10 columns in total, the shaded area represents 110\frac{1}{10} of the total area.

Finally, the fraction 110\frac{1}{10} can be expressed as the decimal 0.10.1.

Therefore, the numerical value of the shaded area is 0.10.1.

3

Final Answer

0.1

Key Points to Remember

Essential concepts to master this topic
  • Grid Analysis: Count total divisions and shaded divisions first
  • Technique: Express as fraction then convert: 110=0.1 \frac{1}{10} = 0.1
  • Check: Verify decimal makes sense: 1 out of 10 equals 0.1 ✓

Common Mistakes

Avoid these frequent errors
  • Counting squares instead of the actual shaded portion
    Don't count individual grid squares when only part of the area is shaded = wrong fraction! This leads to answers like 1 instead of 0.1. Always identify what fraction of the total area is actually shaded.

Practice Quiz

Test your knowledge with interactive questions

Determine the number of tenths in the following number:

1.3

FAQ

Everything you need to know about this question

Why is the answer 0.1 and not just 1?

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The answer represents the fraction of the total area that is shaded, not the number of shaded sections. Since 1 out of 10 columns is shaded, that's 110=0.1 \frac{1}{10} = 0.1 of the whole area.

How do I convert fractions to decimals quickly?

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Divide the numerator by the denominator! For 110 \frac{1}{10} , divide 1 ÷ 10 = 0.1. Remember: tenths become one decimal place, hundredths become two decimal places.

What if the grid had different divisions?

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The same process applies! Count the total divisions, count the shaded divisions, then write as a fraction and convert to decimal.

Can I leave my answer as a fraction?

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While 110 \frac{1}{10} is mathematically correct, the question asks for the numerical value, which typically means decimal form: 0.1.

How do I know I'm reading the grid correctly?

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Look for the colored/shaded region and count how many equal parts it covers. Then count the total number of equal parts in the entire grid.

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