Decimal Fractions Practice Problems & Meaning Worksheets

Master decimal fractions with interactive practice problems. Learn place value, reading decimals, and real-world applications through step-by-step examples and exercises.

📚Practice Decimal Fractions and Build Mathematical Confidence
  • Identify place values in decimal numbers (tenths, hundredths, thousandths)
  • Read and write decimal numbers using proper mathematical terminology
  • Place decimal points correctly to represent specific place values
  • Convert between fraction and decimal representations of numbers
  • Apply decimal concepts to real-world situations like temperature and weight
  • Recognize equivalent decimal forms with trailing zeros

Understanding Decimal Fractions' Meaning

Complete explanation with examples

A decimal number is a way to represent any number using a base-10 place value system. The decimal point separates the whole number part from the fractional part. To the left of the decimal point are whole numbers (ones, tens, hundreds, etc.), and to the right are fractional parts (tenths, hundredths, thousandths, etc.).

The decimal point (or decimal comma in some areas) divides the number in the following way:

A1 - Meaning of the decimal number

For example, when checking a fever, on the thermometer there is a number like 37.537.5 or 36.436.4.

The point that separates the figures is the decimal point, therefore, the number in question is a decimal number.
When we weigh ourselves, we step on the scale and, also in this case, the very same decimal number appears!
The weight is shown with the decimal point and expresses, in a clear and simple way, a number that is not whole.

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 tenths in the following number:

1.3

Step-by-Step Solution

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

  • Step 1: Understand the problem of finding the number of tenths in 1.3.
  • Step 2: Note that the decimal number 1.3 is composed of the whole number 1 and the decimal fraction 0.3.
  • Step 3: Recognize that the tenths place is the first digit after the decimal point.

Now, let's work through each step:

Step 1: The problem asks us to count the number of tenths in the decimal number 1.3. This involves understanding the place value of each digit.

Step 2: In the decimal 1.3, the digit '1' represents the whole number and does not contribute to the count of tenths. The digit '3' is in the tenths place.

Step 3: Since the digit '3' is in the tenths place, it denotes 3 tenths or the fraction 310\frac{3}{10}.

Therefore, the number of tenths in 1.3 is 3 3 .

Answer:

3

Video Solution
Exercise #2

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
Exercise #3

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 #4

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 #5

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

Frequently Asked Questions

What is a decimal fraction and how does it differ from a regular fraction?

+
A decimal fraction is a way to represent parts of a whole using a decimal point instead of a fraction bar. While a regular fraction like 3/4 uses a numerator and denominator, a decimal fraction like 0.75 uses place value positions after the decimal point to show the same value.

How do you read decimal numbers correctly?

+
There are two ways: 1) Read each digit separately with 'point' (e.g., 3.56 as 'three point five six'), or 2) Read the whole part, say 'and,' then read the decimal part based on the last digit's place value (e.g., 3.56 as 'three and fifty-six hundredths').

What do the positions after the decimal point represent?

+
The first position after the decimal point represents tenths, the second represents hundredths, and the third represents thousandths. For example, in 4.586, the 5 is in the tenths place, 8 is in the hundredths place, and 6 is in the thousandths place.

Why can you add zeros to the end of a decimal without changing its value?

+
Adding zeros to the right of the last digit in a decimal doesn't change the value because those positions represent smaller and smaller fractional parts that equal zero. For example, 0.5 = 0.50 = 0.500 because the additional zeros don't add any actual value.

Where do we use decimal numbers in everyday life?

+
Decimal numbers appear frequently in daily life including: • Body temperature readings (37.5°C) • Weight measurements on scales • Money amounts ($12.45) • Sports statistics and measurements • Cooking measurements and recipes

How do you place a decimal point to make a digit represent a specific place value?

+
To make a digit represent tenths, place the decimal point immediately before that digit. For hundredths, place it two positions before, and for thousandths, three positions before. For example, to make 9 represent tenths in 76593, write it as 765.93.

What's the difference between tens and tenths in decimal numbers?

+
Tens are whole number place values to the left of the decimal point (10, 20, 30), while tenths are fractional parts to the right of the decimal point (0.1, 0.2, 0.3). The 's' ending indicates fractional parts: tenths (1/10), hundredths (1/100), thousandths (1/1000).

How do decimal fractions help in understanding parts of a whole?

+
Decimal fractions make it easy to express and calculate with parts of a whole using our base-10 number system. Instead of working with complex fractions, decimals let us use familiar place value concepts to represent precise measurements and calculations in science, finance, and daily life.

More Decimal Fractions' Meaning Questions

Continue Your Math Journey

Practice by Question Type