Decimal Reduction and Expansion Practice Problems

Master reducing and expanding decimal numbers with step-by-step practice problems. Learn when decimals are equal and how trailing zeros work in mathematics.

๐Ÿ“šPractice Reducing and Expanding Decimal Numbers
  • Identify when decimal numbers with trailing zeros are equal
  • Reduce decimal numbers by removing unnecessary trailing zeros
  • Expand decimal numbers by adding zeros to the right
  • Compare decimal values like 0.4 and 0.40 accurately
  • Understand place value positions in tenths, hundredths, and thousandths
  • Apply decimal reduction and expansion rules in real problems

Understanding Reduction and Expansion of Decimal Fractions

Complete explanation with examples

The topic of reducing and expanding decimal numbers is extremely easy.
All you need to remember is the following phrase:

If we add the digit 0 at the end of a decimal number (to the right), the value of the decimal number will not change.

What does this tell us?

Let's look at some examples:
We can compare 0.40.4 and 0.400.40 precisely because of the phrase we saw earlier.
In fact, 44 tenths is equivalent to 4040 hundredths.
Similarly, we can compare 2.562.56 and the decimal number2.5602.560 and also the decimal number 2.56002.5600

What does this have to do with the simplification and amplification of decimal numbers?

When we compare these decimal numbers and do not calculate the meaning of 00, we are simplifying and expanding without realizing it.

Detailed explanation

Practice Reduction and Expansion of Decimal Fractions

Test your knowledge with 11 quizzes

Reduce the following fraction:

\( 0.10200 \)

Examples with solutions for Reduction and Expansion of Decimal Fractions

Step-by-step solutions included
Exercise #1

Reduce the following fraction:

0.25 0.25

Step-by-Step Solution

To reduce the fraction 0.25 0.25 , we note that it is already in its simplest form as a decimal fraction and cannot be reduced further. Therefore, the reduced form is 0.25 0.25 itself.

Answer:

0.25 0.25

Exercise #2

Reduce the following fraction:

0.40 0.40

Step-by-Step Solution

To reduce the fraction 0.40 0.40 , we recognize that trailing zeros in decimals do not affect their value. Thus, we can remove the zero to obtain 0.4 0.4 . Therefore, 0.40=0.4 0.40 = 0.4 .

Answer:

0.4 0.4

Exercise #3

Reduce the following fraction:

0.50 0.50

Step-by-Step Solution

To reduce the fraction 0.50 0.50 , you need to express it in its simplest form by removing any trailing zeros. The trailing zero in 0.50 0.50 doesn't change the value of the number, as it represents tenths. Without the zero, the number is reduced to 0.5 0.5 , which is the simplest form.

Answer:

0.5 0.5

Exercise #4

Reduce the following fraction:

0.56000 0.56000

Step-by-Step Solution

To reduce the decimal fraction 0.56000 0.56000 , we eliminate trailing zeros that have no significance after the decimal point. Thus, 0.56000 0.56000 becomes 0.56 0.56 .
Therefore, the reduced fraction is 0.56 0.56 .

Answer:

0.56 0.56

Exercise #5

Reduce the following fraction:

0.5 0.5

Step-by-Step Solution

To reduce 0.5 0.5 , recognize that it's already in its simplest form as a decimal fraction.

When expressed as a fraction of 1, 0.5 0.5 is equivalent to 12 \frac{1}{2} , which means 0.5 0.5 is simplified.

Answer:

0.5 0.5

Frequently Asked Questions

Everything you need to know about Reduction and Expansion of Decimal Fractions

What is decimal reduction and expansion?

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Decimal reduction removes trailing zeros from the right of a decimal number without changing its value (8.70 becomes 8.7). Decimal expansion adds zeros to the right of a decimal number, also without changing its value (0.4 becomes 0.40).

Why are 0.4 and 0.40 equal?

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Both decimals represent the same value because 4 tenths equals 40 hundredths. Adding or removing trailing zeros to the right of a decimal point doesn't change the number's value - it's the fundamental rule of decimal equivalence.

How do you reduce a decimal number?

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To reduce a decimal number, simply remove any trailing zeros from the right side after the decimal point. For example: 2.560 reduces to 2.56, and 8.70 reduces to 8.7.

When should you expand decimal numbers?

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Expand decimal numbers when you need to: 1) Compare decimals with different decimal places, 2) Perform calculations requiring the same number of decimal places, 3) Match a specific format requirement in math problems.

Do trailing zeros affect decimal value?

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No, trailing zeros after the decimal point do not change a number's value. The decimal 5.3 has the same value as 5.30, 5.300, or 5.3000 because zeros in these positions represent empty place values.

What's the difference between 0.7 and 0.07?

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These are completely different values. 0.7 equals 7 tenths, while 0.07 equals 7 hundredths. The zero between the decimal point and 7 in 0.07 is not a trailing zero - it's a placeholder that affects the number's value.

How do place values work in decimal expansion?

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In decimal numbers, each position represents a specific place value: tenths (0.1), hundredths (0.01), thousandths (0.001), etc. When expanding 2.5 to 2.500, you're showing 2 ones, 5 tenths, 0 hundredths, and 0 thousandths.

Can you reduce all decimal numbers?

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You can only reduce decimal numbers that have trailing zeros. Numbers like 3.25 or 0.147 cannot be reduced because they don't end in zero. However, 3.250 can be reduced to 3.25.

More Reduction and Expansion of Decimal Fractions Questions

Click on any question to see the complete solution with step-by-step explanations

Reduction and Expansion of Decimal Fractions

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Continue Your Math Journey

Master Reduction and Expansion of Decimal Fractions first, then advance to these related topics that build on your fraction skills

Suggested Topics to Practice in Advance

What is a Decimal Number?Decimal fraction remainderRemainders

Topics Learned in Later Sections

Decimal FractionsConverting a Decimal Fraction to a Mixed NumberConverting a simple fraction to decimal - how to calculate?Addition and Subtraction of Decimal NumbersComparison of Decimal NumbersConverting Decimals to Fractions

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