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

Determine the number of ones in the following number:

0.81

Examples with solutions for Decimal Fractions' Meaning

Step-by-step solutions included
Exercise #1

Which figure represents 0.1?

Step-by-Step Solution

The task is to determine which of the given figures correctly represents the decimal fraction 0.1.

To interpret 0.1, we recognize it as 110\frac{1}{10}. This indicates that in a graphical representation of 10 equal parts, 1 part should be shaded. Each figure is assumed to be divided into such equal parts.

Let's analyze the options:

  • Choice 1: Shows 10 equal divisions with 1 part shaded. This potentially represents 0.1 since it shades exactly 1 of 10 parts.
  • Choice 2: Shows 10 equal divisions with more than 1 part shaded. Thus, it represents more than 0.1.
  • Choice 3: Shows 10 equal divisions with numerous parts shaded. It represents a number greater than 0.1.
  • Choice 4: Shows a full shading, representing 1 (i.e., shading all 10 parts), clearly not 0.1.

Hence, the correct choice that correspond to 0.1 is Choice 1. This figure accurately shades exactly 1 out of 10 equal segments.

Therefore, the solution to the problem indicates that choice 1 correctly represents the decimal fraction 0.1.

Answer:

Exercise #2

Which figure represents seven tenths?

Step-by-Step Solution

To solve the problem of identifying which figure represents seven tenths, follow these steps:

  • Step 1: Understand that the problem requires identification of a geometric representation for the fraction 710\frac{7}{10} or decimal 0.7.
  • Step 2: Each figure is divided into ten equal segments, representing one tenth each.
  • Step 3: Carefully count the number of segments filled or shaded in each figure.

Now, let's apply these steps:

Step 1: We note that each figure is evenly divided into ten parts.

Step 2: By inspecting each option, you can see which has exactly seven segments shaded. This corresponds directly to seven out of ten segments, or seven tenths.

Step 3: Upon review, the figure corresponding to choice 3 shows exactly seven shaded segments out of ten.

Therefore, the solution to the problem is eminently found as choice 3, representing seven tenths.

Answer:

Exercise #3

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 #4

Determine the number of ones in the following number:

0.73

Step-by-Step Solution

To solve this problem, let's carefully examine the decimal number 0.73 0.73 digit by digit:

  • The first digit after the decimal point is 7 7 .
  • The second digit after the decimal point is 3 3 .

We observe that there are no digits in the sequence of 0.73 0.73 that are the number '1'. Therefore, there are no '1's in the decimal number 0.73 0.73 .

Thus, the number of ones in the number 0.73 0.73 is 0.

The correct choice, given the options, is choice id 1: 0.

Answer:

0

Video Solution
Exercise #5

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

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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