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.

๐Ÿ“šMaster 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 numerical value of the shaded area:

Examples with solutions for Decimal Fractions' Meaning

Step-by-step solutions included
Exercise #1

Determine the number of ones in the following number:

0.81

Step-by-Step Solution

To solve this problem, we need to examine the decimal number 0.810.81 and count the number of '1's present:

  • The first digit after the decimal point is 88.
  • The second digit after the decimal point is 11.

Now, count the number of '1's in 0.810.81:

There is only one '1' in the entire number 0.810.81 because it appears only once after the decimal point.

Thus, the total number of ones in 0.810.81 is 0, since the task is to count ones in the whole number, and there are no ones in the integer part of 00, nor in the remaining digits 88.

Therefore, the solution to the problem is 00, which corresponds to choice 3.

Answer:

0

Video Solution
Exercise #2

Determine the number of hundredths in the following number:

0.96

Step-by-Step Solution

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

  • Step 1: Define the place value of each digit in the decimal number.
  • Step 2: Identify the specific digit in the hundredths place.
  • Step 3: Determine the number of hundredths in 0.96.

Now, let's work through each step:

Step 1: Consider the decimal number 0.960.96. In decimal representation, the digit immediately after the decimal point represents tenths, and the digit following that represents hundredths.

Step 2: In the number 0.960.96, the digit 99 is in the tenths place, and the digit 66 is in the hundredths place.

Step 3: Therefore, the number of hundredths in 0.960.96 is 66.

Thus, the solution to the problem is that there are 6 hundredths in the number 0.960.96.

Answer:

6

Video Solution
Exercise #3

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 #4

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
Exercise #5

Determine the number of ones in the following number:

0.4

Step-by-Step Solution

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

  • Examine the given number 0.4.
  • Identify and list all digits represented in this decimal.
  • Count the occurrences of the digit '1'.

Now, let's work through each step:
Step 1: The number given is 0.4. This number is composed of the digits '0', '.', and '4'.
Step 2: Identify any '1's among these digits. There are no '1's in this sequence of digits.
Step 3: Thus, the count of the digit '1' in the number 0.4 is zero.

Therefore, the number of ones in the number 0.4 is 00.

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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