Decimal Fractions Practice: Master Decimal Remainders

Practice identifying decimal remainders and decimal fractions with step-by-step problems. Master the concept of decimal parts vs whole numbers through guided exercises.

📚Master Decimal Fractions with Interactive Practice Problems
  • Identify decimal remainders in numbers like 45.6, 8.449, and 0.5
  • Distinguish between whole number parts and decimal parts in decimal fractions
  • Recognize when decimal numbers have zero remainders or no remainders
  • Handle special cases like 67.0003 where zeros appear after decimal points
  • Convert decimal remainders to proper decimal fraction notation
  • Practice with real-world examples involving division and fractional parts

Understanding Decimal Fractions' Meaning

Complete explanation with examples

Decimal remainder

A decimal remainder or decimal fraction is everything that appears to the right of the decimal point.
When the whole number is 00, the entire number (not just what appears to the right of the decimal point) is the remainder.

Mathematical concept of division showing the whole number and remainder. Visual representation to explain quotient and remainder in long division. Fundamental arithmetic concept

Detailed explanation

Practice Decimal Fractions' Meaning

Test your knowledge with 28 quizzes

Which figure represents seven tenths?

Examples with solutions for Decimal Fractions' Meaning

Step-by-step solutions included
Exercise #1

Determine the numerical value of the shaded area:

Step-by-Step Solution

To solve this problem, let's analyze the shaded area in terms of grid squares:

  • Step 1: The top rectangle in the grid is completely filled. Let's count the shaded squares horizontally: There are 10 squares across aligned vertically in 1 row, giving 11 as the shaded area.
  • Step 2: The bottom rectangle is partially filled. Observe it spans 66 squares horizontally by 11 square height in the grid row. The shaded area will, therefore, be 0.60.6 as it spans only 60%60\% of the horizontal extent.
  • Step 3: Add both shaded areas of the rectangles from step 1 and step 2: 11 (top) and 0.60.6 (bottom).

Thus, the total shaded area is 1+0.6=1.61 + 0.6 = 1.6.

Therefore, the solution to the problem is 1.61.6.

Answer:

1.6

Exercise #2

Determine the numerical value of the shaded area:

Step-by-Step Solution

To solve this problem, we'll follow a few simple steps to calculate the shaded area by counting strips and converting to a decimal:

  • Step 1: Identify the total number of vertical strips in the entire rectangle. From the diagram, there are 10 strips in total.
  • Step 2: Count the number of shaded vertical strips. According to the diagram, 5 strips are shaded.
  • Step 3: Write the fraction of the shaded area relative to the total area. The fraction is 510\frac{5}{10}.
  • Step 4: Simplify the fraction, which is already simplified, and then convert it to a decimal. 510=0.5\frac{5}{10} = 0.5.

Therefore, the solution to the problem is 0.5 0.5 .

Answer:

0.5

Exercise #3

Determine the numerical value of the shaded area:

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.

Answer:

0.1

Exercise #4

Determine the numerical value of the shaded area:

Step-by-Step Solution

To solve this problem, let's follow the outlined plan:

  • Step 1: Count the number of shaded sections.
  • Step 2: Count the total number of sections in the rectangle.
  • Step 3: Express the number of shaded sections as a fraction of the total sections.
  • Step 4: Convert this fraction to a decimal to find the numerical value.

Now, let's apply these steps:
Step 1: The given diagram shows that there are 4 vertical stripes shaded.
Step 2: The total number of vertical stripes (including both shaded and unshaded) is 10.
Step 3: The fraction of shaded area is 410\frac{4}{10}.
Step 4: Convert 410\frac{4}{10} to a decimal. This equals 0.40.4.

Therefore, the numerical value of the shaded area is 0.4.

Answer:

0.4

Exercise #5

Determine the number of ones in the following number:

0.07

Step-by-Step Solution

To solve this problem, we'll examine the given decimal number, 0.070.07, to identify how many '1's it contains.

Let's break down the number 0.070.07:

  • The digit to the left of the decimal is 00, which is the ones place. It is not '1'.
  • The first digit after the decimal point is 00, which represents tenths. This is also not '1'.
  • The next digit is 77, which represents hundredths. This digit is also not '1'.

None of the digits in the number 0.070.07 are equal to '1'.

Therefore, the number of ones in 0.070.07 is 0.

Answer:

0

Video Solution

Frequently Asked Questions

What is a decimal remainder in a decimal fraction?

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A decimal remainder is everything that appears to the right of the decimal point in a decimal number. For example, in 45.6, the decimal remainder is 6 (or 0.6). When the whole number is 0, like in 0.5, the entire number is considered the remainder.

How do I identify the decimal part vs whole number part?

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Everything to the left of the decimal point is the whole number part, and everything to the right is the decimal part (remainder). In 12.34: whole number = 12, decimal remainder = 0.34.

What is the decimal remainder in 45.06?

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The decimal remainder in 45.06 is 0.06, not 6 or 0.6. You must include all digits after the decimal point, including zeros, as they are significant when identifying remainders.

When does a decimal number have zero remainder?

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A decimal number has zero remainder when there are no digits after the decimal point (like 12) or when only zeros appear after the decimal point (like 12.0000). In both cases, the remainder is 0.

What makes 0.5 different from other decimal fractions?

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In 0.5, the entire number is a remainder because the whole number part is 0. This represents a pure fraction (like 1/2) with no whole number component, so the complete decimal 0.5 is the remainder.

How do I handle decimal numbers like 67.0003?

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In 67.0003, the decimal remainder is 0.0003, not just 3. You must include all digits after the decimal point, including the zeros, to maintain the correct place value and meaning of the decimal fraction.

What are common mistakes when identifying decimal remainders?

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Common mistakes include: 1) Ignoring zeros after the decimal point (writing 6 instead of 0.06 for 45.06), 2) Not adding 0. before the decimal part when expressing remainders, 3) Forgetting that in numbers like 0.25, the entire number is the remainder.

Why is understanding decimal remainders important in math?

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Understanding decimal remainders helps with division problems, converting fractions to decimals, working with money and measurements, and solving real-world problems involving parts of wholes. It's fundamental for advanced math concepts like percentages and ratios.

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