Solved Exercises on Decimal Notation for Fractions in Grade 4

Master decimal notation for fractions: converting fractions to decimals, place value understanding, and practical applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Converting Simple Fractions to Decimals
Exercise 1
Convert the fraction 3/10 to decimal notation.
Definition:

Fraction: A number representing parts of a whole, written as numerator/denominator

Decimal notation: A way to write fractions using place value positions after the decimal point

Conversion method:
  1. Identify the denominator (the bottom number)
  2. Look for denominators that are powers of 10 (10, 100, 1000, etc.)
  3. Place the numerator in the appropriate decimal place
Fraction
3/10
Decimal
0.3
Step 1: Analyze the fraction

The fraction 3/10 has numerator 3 and denominator 10

Step 2: Understand the denominator

Denominator 10 means we're dealing with tenths

Step 3: Place the numerator

Since the denominator is 10, the numerator 3 goes in the tenths place

Step 4: Write in decimal form

3 tenths = 0.3

3/10 = 0.3
Final answer:

3/10 = 0.3

Applied rules:

• Place Value Rule: Denominators of 10 correspond to tenths place

• Numerator Placement: Numerator goes in the place matching the denominator

• Decimal Point: Goes to the left of the tenths digit

Tip: Remember: denominator 10 = tenths place, denominator 100 = hundredths place
2 Converting Hundredths to Decimals
Exercise 2
Convert the fraction 47/100 to decimal notation.
Definition:

Hundredths: Parts of a whole divided into 100 equal parts

Decimal place value: Each position after the decimal represents a power of ten

Fraction
47/100
Decimal
0.47
Step 1: Identify the denominator

The denominator is 100, which corresponds to hundredths

Step 2: Break down the numerator

47 has 4 tens and 7 ones

Step 3: Place digits in correct positions

4 goes in the tenths place, 7 goes in the hundredths place

Step 4: Write the decimal

47 hundredths = 0.47

47/100 = 0.47
Final answer:

47/100 = 0.47

Applied rules:

• Denominator Rule: 100 in denominator means hundredths place

• Digit Placement: Tens digit goes in tenths place, ones digit in hundredths place

• Leading Zero: Always include 0 before decimal point for values less than 1

Tip: Count zeros in denominator to know how many decimal places (10 = 1 place, 100 = 2 places, 1000 = 3 places)
3 Mixed Number to Decimal
Exercise 3
Convert the mixed number 2 3/10 to decimal notation.
Definition:

Mixed number: A combination of a whole number and a fraction

Decimal notation: Combines whole numbers with decimal fractions

Mixed Number
2 3/10
Conversion
2 + 0.3
Result
2.3
Step 1: Separate whole and fractional parts

2 3/10 = 2 + 3/10

Step 2: Convert fractional part

3/10 = 0.3 (as shown in Exercise 1)

Step 3: Combine whole and decimal parts

2 + 0.3 = 2.3

Step 4: Verify the result

2.3 means 2 wholes and 3 tenths

2 3/10 = 2.3
Final answer:

2 3/10 = 2.3

Applied rules:

• Separation Rule: Separate whole number from fraction first

• Conversion Rule: Convert fraction to decimal separately

• Addition Rule: Add whole number to decimal part

Tip: For mixed numbers, keep the whole number as is and convert only the fractional part
Decimal Place Value System
0.1 = 1/10
One Tenth
Tenths
0.1 = 1/10
One place after decimal
Hundredths
0.01 = 1/100
Two places after decimal
Thousandths
0.001 = 1/1000
Three places after decimal
Key definitions:

Decimal point: Separates whole numbers from fractional parts

Place value: Position of a digit determines its value

Equivalent fractions: Different fractions that represent the same value

Conversion methodology:
  1. Identify denominator: Look for powers of 10 (10, 100, 1000...)
  2. Count decimal places: Zeros in denominator = decimal places needed
  3. Place numerator: Put digits in correct decimal positions
  4. Verify result: Check that decimal equals original fraction
Tip 1: Denominator 10 = 1 decimal place, 100 = 2 decimal places, 1000 = 3 decimal places
Tip 2: Always include leading zero for decimals less than 1 (write 0.5, not .5)
Tip 3: For mixed numbers, keep whole number separate and convert only the fraction part
Tip 4: Use visual models (grids, base-ten blocks) to reinforce decimal concepts
Common errors: Forgetting leading zero, misplacing decimal point, confusing tenths with hundredths.
Memorization tip: "Ten has one zero, tenths has one decimal place; hundred has two zeros, hundredths has two decimal places."
Place value relationships:

• 1 = 10/10 = 100/100 (whole number equals any equivalent fraction)

• 0.1 = 1/10 (one tenth)

• 0.01 = 1/100 (one hundredth)

• 0.001 = 1/1000 (one thousandth)

Solution: Exercises 4 to 5
4 Complex Fraction Conversion
Exercise 4
Convert the fraction 127/100 to decimal notation.
Definition:

Improper fraction: A fraction where numerator is greater than denominator

Decimal conversion: May result in a whole number plus a decimal fraction

Fraction
127/100
Division
127 ÷ 100
Decimal
1.27
Step 1: Analyze the fraction

127/100 has numerator 127 and denominator 100

Step 2: Determine how many whole units

127 ÷ 100 = 1 remainder 27, so we have 1 whole unit

Step 3: Handle the remainder

The remainder 27 over 100 gives us 27 hundredths

Step 4: Combine whole and decimal parts

1 whole + 27 hundredths = 1.27

127/100 = 1.27
Final answer:

127/100 = 1.27

Applied rules:

• Division Rule: When numerator > denominator, divide to find whole units

• Remainder Rule: Remainder becomes the decimal fraction part

• Combination Rule: Combine whole number with decimal fraction

Tip: For improper fractions, divide numerator by denominator to find whole units and remainder
5 Decimal Comparison and Ordering
Exercise 5
Order these numbers from least to greatest: 0.45, 3/10, 0.6, 7/100
Definition:

Decimal comparison: Comparing values by examining place values systematically

Ordering decimals: Arranging numbers from smallest to largest or vice versa

Numbers
0.45, 3/10, 0.6, 7/100
Convert
0.45, 0.3, 0.6, 0.07
Ordered
0.07, 0.3, 0.45, 0.6
Step 1: Convert all to decimal form

3/10 = 0.3 and 7/100 = 0.07

So we have: 0.45, 0.3, 0.6, 0.07

Step 2: Compare tenths place first

0.07 (0 tenths), 0.3 (3 tenths), 0.45 (4 tenths), 0.6 (6 tenths)

Step 3: Arrange in order

0.07 < 0.3 < 0.45 < 0.6

Step 4: Convert back to original form

7/100, 3/10, 0.45, 0.6

7/100 < 3/10 < 0.45 < 0.6
Final answer:

From least to greatest: 7/100, 3/10, 0.45, 0.6

Applied rules:

• Conversion Rule: Convert all numbers to same form (decimals) for easy comparison

• Place Value Rule: Compare from left to right starting with highest place value

• Comparison Rule: Larger digits in higher place values make larger numbers

Tip: Always convert mixed forms to the same format (decimals) before comparing
Decimal Notation Fundamentals and Practice
1/10 = 0.1, 1/100 = 0.01
Basic Decimal Equivalents
Key definitions:

Decimal notation: A way to express fractions using a decimal point and place value system

Place value: The value of a digit based on its position in a number

Equivalent fractions: Different fractions that represent the same amount

Complete methodology:
  1. Identify the fraction: Recognize numerator and denominator
  2. Check denominator: See if it's a power of 10 (10, 100, 1000...)
  3. Apply conversion: Use place value system to write decimal
  4. Verify result: Check by converting back to fraction
Tip 1: To convert, count zeros in denominator to determine decimal places needed.
Tip 2: For denominators that aren't powers of 10, try to rewrite as equivalent fraction with denominator of 10, 100, or 1000.
Tip 3: Use visual aids like grids or base-ten blocks to understand the relationship between fractions and decimals.
Tip 4: Always include a leading zero for decimals less than 1 (write 0.5, not .5).
Common errors: Forgetting leading zero, misplacing decimal point, confusing tenths with hundredths.
Memory aid: "Ten has one zero, tenths has one decimal place; hundred has two zeros, hundredths has two decimal places."
Decimal place value rules:

• Tenths place: 1 digit after decimal point (0.1 = 1/10)

• Hundredths place: 2 digits after decimal point (0.01 = 1/100)

• Thousandths place: 3 digits after decimal point (0.001 = 1/1000)

• When comparing decimals, start from the leftmost digit and compare place by place

Visualizing Decimal Fractions
Understanding Decimal Values
Visual representation of common decimal fractions:
0.1 = 1/10 (one tenth)
0.25 = 25/100 (twenty-five hundredths)
0.5 = 5/10 (five tenths)
0.75 = 75/100 (seventy-five hundredths)

Analysis: The chart shows how decimal fractions relate to their fractional equivalents and visual representations.

  • 0.1 represents one part out of ten equal parts
  • 0.25 represents 25 parts out of 100 equal parts
  • 0.5 represents half of a whole unit
  • 0.75 represents three-quarters of a whole unit

Questions & Answers

Question: I don't understand why 3/10 equals 0.3. Why isn't it 0.30 since 30/100 also equals 3/10?

Answer: Great observation! You're absolutely right that 3/10 = 30/100, and both are equivalent to 0.3.

  • 3/10 means 3 parts out of 10 equal parts, which directly converts to 0.3 (3 in the tenths place)
  • 30/100 means 30 parts out of 100 equal parts, which converts to 0.30 (3 in the tenths place and 0 in the hundredths place)
  • Both 0.3 and 0.30 represent the same value! The extra zero doesn't change the value.

However, when we have a denominator of 10, we typically write the decimal with just one place after the decimal point (0.3) because it's simpler. Both 0.3 and 0.30 are correct, but 0.3 is the more concise way to write it.

Question: How do I know where to put the decimal point when converting 47/100 to decimal?

Answer: There's a simple pattern to follow based on the denominator:

  • Count the zeros in the denominator: 100 has 2 zeros
  • This means you need 2 decimal places: _._ _
  • Place the numerator (47) in the last 2 places: 0.47

Think of it this way: the denominator tells you how many equal parts the whole is divided into. 100 means hundredths, so the decimal needs to show hundredths. Since 47/100 means 47 hundredths, you write 0.47.

The 4 goes in the tenths place (because 47 has 4 tens) and the 7 goes in the hundredths place (because 47 has 7 ones).

Question: I'm confused about mixed numbers like 2 3/10. Why does it become 2.3 and not 2.3 or something else?

Answer: The mixed number 2 3/10 means 2 wholes AND 3 tenths. Let's break it down:

  • The whole number part (2) stays to the left of the decimal point
  • The fractional part (3/10) gets converted to decimal form (0.3)
  • Combine them: 2 + 0.3 = 2.3

The decimal point separates the whole number part from the fractional part. So 2.3 literally means 2 wholes and 3 tenths, which is exactly what 2 3/10 represents.

Think of it like money: $2.30 means 2 dollars and 30 cents, which is similar to having 2 wholes and 3 tenths.