Decimal Fractions Practice Problems - Advanced Math

Master advanced decimal fractions with step-by-step practice problems. Convert decimals to fractions, multiply and divide decimals, and solve real-world applications.

📚Master Advanced Decimal Fractions with Interactive Practice
  • Convert decimal numbers to fractions and mixed numbers with confidence
  • Multiply and divide decimal numbers using vertical methods and shortcuts
  • Compare decimal numbers systematically using place value understanding
  • Add and subtract decimals by aligning decimal points correctly
  • Apply decimal point movement rules for multiplication and division by 10, 100, 1000
  • Solve real-world problems involving decimal measurements and conversions

Understanding Decimal Fractions - Advanced

Complete explanation with examples

Decimal Numbers

Meaning of the Decimal Number

The decimal number represents, through the decimal point (or comma in certain countries), a simple fraction or a number that is not whole.
The decimal point divides the number in the following way:

A - Decimal number

You can read more in the assigned extended article


Detailed explanation

Practice Decimal Fractions - Advanced

Test your knowledge with 88 quizzes

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

38.15-122.3

Examples with solutions for Decimal Fractions - Advanced

Step-by-step solutions included
Exercise #1

Determine whether the exercise is correctly written or not.

True or false:

The positions of the decimal points correspond.

21.52+3.4

Step-by-Step Solution

First let's fill in the zeros in the empty spaces as follows:

21.52+03.40 21.52\\+03.40\\ Note that the decimal points are written one below the other.

Therefore, the positions of the decimal points correspond and thus the exercise is written in the correct form.

Answer:

True

Video Solution
Exercise #2

Determine whether the exercise is written correctly:

Is the position of the decimal point correct in each number?

6.31+216.222

Step-by-Step Solution

First let's fill the zeros in the empty space as follows:

006.310+216.222  006.310\\+216.222\\\

Here We should note that the decimal points are written one below the other.

Therefore, the exercise is written in the appropriate form.

Answer:

Yes

Video Solution
Exercise #3

Reduce the following fraction:

0.7000 0.7000

Step-by-Step Solution

If you have a fraction like 0.7000 0.7000 , you can simplify it by removing all the trailing zeros. Thus, it reduces down to 0.7 0.7 . All the trailing zeros to the right of the decimal point in a number can be eliminated without changing the value of the number.

Answer:

0.7 0.7

Exercise #4

-0.9=

Step-by-Step Solution

Let's solve the subtraction problem step by step:

  • Step 1: Align the decimal numbers. The subtraction is 1.80.91.8 - 0.9. Both numbers have their decimal points aligned.
  • Step 2: Subtract the numbers starting from the tenths place: 88 (in 1.81.8) minus 99 (in 0.90.9). This requires borrowing.
  • Step 3: Regroup, take 11 from the units place of 1.81.8, which then becomes 0.8+100.8 + 10 (or 1010 tenths), thus 1818 tenths. Subtract 99 tenths from 1818 tenths, resulting in 99 tenths.
  • Step 4: The units digit of 1.81.8 now, after borrowing, is 00. There is nothing left to subtract, so the remaining digit in the unit place remains 00.
  • Step 5: Therefore, the answer obtained is 0.90.9.

Thus, the solution to the problem is 0.9\mathbf{0.9}.

Answer:

0.9

Exercise #5

Determine whether the exercise is correctly written or not.

3.05+213.22

Step-by-Step Solution

Note that the decimal points are not written one below the other. They do not correspond.

Therefore, the exercise is not written correctly.

Answer:

Not true

Video Solution

Frequently Asked Questions

How do you convert a decimal number to a fraction step by step?

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To convert a decimal to a fraction: 1) Count the decimal places, 2) Write the decimal number as the numerator, 3) Use the appropriate denominator (10 for tenths, 100 for hundredths, 1000 for thousandths), 4) Simplify the fraction if possible. For example, 0.75 = 75/100 = 3/4.

What are the rules for multiplying decimal numbers?

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When multiplying decimals: 1) Multiply the numbers ignoring decimal points, 2) Count total decimal places in both numbers, 3) Place the decimal point in the answer so it has the same total number of decimal places. For example, 2.5 × 1.2 = 3.0 (1 + 1 = 2 decimal places).

How do you compare decimal numbers correctly?

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Compare decimals by: 1) First comparing whole number parts - larger whole number wins, 2) If whole parts are equal, compare digits after decimal point from left to right (tenths, then hundredths, etc.), 3) The first different digit determines which decimal is larger.

What is the shortcut for multiplying decimals by 10, 100, or 1000?

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Move the decimal point to the right: • 1 place for ×10 • 2 places for ×100 • 3 places for ×1000. For division, move left the same number of places. Example: 4.56 × 100 = 456.0

How do you add and subtract decimal numbers without mistakes?

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Follow these steps: 1) Write numbers vertically with decimal points aligned, 2) Add zeros if needed to make equal decimal places, 3) Add or subtract normally from right to left, 4) Keep decimal point in same position in answer.

What is a repeating decimal and how do you identify it?

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A repeating decimal has digits that repeat infinitely in a pattern after the decimal point. Examples include 0.333... (1/3) or 0.142857142857... (1/7). You can identify them when dividing fractions that don't result in terminating decimals.

How do you convert mixed numbers from decimal numbers?

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Steps to convert: 1) Convert decimal to fraction using place value, 2) If numerator is larger than denominator, divide numerator by denominator, 3) Whole number part becomes the mixed number's whole part, 4) Remainder becomes new numerator, denominator stays same.

What are common mistakes students make with decimal operations?

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Common errors include: • Not aligning decimal points in addition/subtraction • Forgetting to count decimal places in multiplication • Moving decimal point wrong direction in division • Not simplifying fraction answers • Misplacing decimal point in final answers

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