Decimal Notation

Grade 4 · decimals · 100 practice problems · read aloud

🔊 Listen to this explanation

Decimal Notation: Understanding Parts of a Whole

Decimals are a special way to write numbers that are less than one, or a mix of whole numbers and parts of a whole. We use them all the time for money ($4.75), measurements (2.5 liters), and scores (9.8). The decimal point (.) separates the whole number from the part of a whole.

🔍 Step-by-Step Guide: Reading Decimals

  1. Find the decimal point. It's the dot between the numbers.
  2. Read the whole number part. These are the numbers to the LEFT of the decimal point.
  3. Say "and" for the decimal point.
  4. Read the digits to the right as if they were a whole number.
  5. Say the place value of the last digit. The first digit after the decimal is the tenths place. The second is the hundredths place.

📚 Visual Examples

Example 1: 3.4

Step 1: Whole number part is 3.
Step 2: The digit after the decimal is 4.
Step 3: The 4 is in the tenths place.
Read as: "three and four tenths." This is like having 3 whole pizzas and 4 slices from a pizza cut into 10 slices.

Example 2: 2.75

Step 1: Whole number part is 2.
Step 2: The digits after the decimal are 75.
Step 3: The 7 is in the tenths place, and the 5 is in the hundredths place.
Read as: "two and seventy-five hundredths." This is like $2.75 — two whole dollars and 75 cents out of 100.

⚠️ Common Mistakes

Misreading the place value: Saying "three point four" is okay, but understanding it as "four tenths" is key. Don't say "three point forty" for 3.4.

Forgetting the "and": The word "and" should only be used for the decimal point. We say "one hundred and two" for 102, but for 102.8, we say "one hundred two and eight tenths."

Confusing digits: 0.5 is five tenths (or one half), not just "point five" without understanding it means 5/10.

💡 Tips & Tricks

  • Money is your best friend! Think of decimals as dollars and cents. $1.23 has 1 whole dollar, 2 dimes (tenths), and 3 pennies (hundredths).
  • Place Value House: Imagine a house. The units, tens, and hundreds live to the LEFT of the decimal point. The tenths and hundredths live to the RIGHT.
  • Zero as a placeholder: A zero before the decimal point (0.6) shows there is no whole number. It's just "six tenths."

🎯 Practice Suggestions

  • Look at price tags in a store or online and read the decimals aloud.
  • Get a ruler and measure objects to the nearest tenth of a centimeter.
  • Draw number lines and practice placing numbers like 0.5, 1.2, and 2.75 in the correct spots.
  • Ask a friend or parent to write down 5 decimals, and you practice reading them correctly.

Practice problems

6 of the 100, worked through step by step — try them before opening the answer.

1 3.45 × 2 = ?

Hint: When multiplying a decimal by a whole number, multiply as if both were whole numbers, then place the decimal point correctly in the result.

Show the answer

Answer: 6.9

  1. Multiply 3.45 by 2 as if they were whole numbers: 345 × 2 = 690
  2. Count the decimal places in the original decimal number. 3.45 has 2 decimal places.
  3. Place the decimal point in the answer so it also has 2 decimal places: 690 becomes 6.90
  4. Simplify by removing the unnecessary zero at the end: 6.90 = 6.9

The answer is 6.9.

2 3.75 × 4.2 = ?

Hint: When multiplying decimals, first multiply as if they were whole numbers, then count the total decimal places in both factors to place the decimal point in the product.

Show the answer

Answer: 15.75

  1. Multiply 3.75 × 4.2 as if they were whole numbers: 375 × 42
  2. 375 × 40 = 15,000
  3. 375 × 2 = 750
  4. Add the partial products: 15,000 + 750 = 15,750
  5. Count the decimal places: 3.75 has 2 decimal places, 4.2 has 1 decimal place, so total of 3 decimal places
  6. Place the decimal point in 15,750 to get 15.750
  7. Remove the trailing zero: 15.75

The answer is 15.75.

3 3.45 × 2.6 = ?

Hint: When multiplying decimals, first multiply as if they were whole numbers, then count the total decimal places in both factors to determine where to place the decimal point in your answer.

Show the answer

Answer: 8.97

  1. Multiply 3.45 × 2.6 as if they were whole numbers: 345 × 26
  2. 345 × 20 = 6,900
  3. 345 × 6 = 2,070
  4. Add the partial products: 6,900 + 2,070 = 8,970
  5. Count the decimal places: 3.45 has 2 decimal places, 2.6 has 1 decimal place, so total is 3 decimal places
  6. Place the decimal point in 8,970 to get 3 decimal places: 8.970
  7. Remove the trailing zero: 8.97

The answer is 8.97.

4 4.25 × 3.2 = ?

Hint: When multiplying decimals, first ignore the decimal points and multiply the numbers as if they were whole numbers. Then count the total decimal places in both original numbers to determine where to place the decimal point in your answer.

Show the answer

Answer: 13.6

  1. Multiply 4.25 × 3.2 as if they were whole numbers: 425 × 32
  2. 425 × 30 = 12,750
  3. 425 × 2 = 850
  4. Add the partial products: 12,750 + 850 = 13,600
  5. Count the decimal places: 4.25 has 2 decimal places, 3.2 has 1 decimal place, so total is 3 decimal places
  6. Place the decimal point in 13,600 to get 13.600
  7. Remove the trailing zero: 13.6

The answer is 13.6.

5 4.25 × 3.6 = ?

Hint: Multiply the numbers as if they were whole numbers, then count the total decimal places in the original numbers to place the decimal point correctly in your answer.

Show the answer

Answer: 15.3

  1. Multiply 4.25 × 3.6 as if they were whole numbers: 425 × 36
  2. 425 × 30 = 12,750
  3. 425 × 6 = 2,550
  4. Add the results: 12,750 + 2,550 = 15,300
  5. Count the decimal places: 4.25 has 2 decimal places, 3.6 has 1 decimal place, so total decimal places = 3
  6. Place the decimal point in 15,300 to get 3 decimal places: 15.300 = 15.3

The answer is 15.3.

6 3.25 + 1.75 = ?

Hint: When adding numbers with decimal points, make sure to align the decimal points and add each place value separately, carrying over when needed.

Show the answer

Answer: 5.00

  1. Write the numbers with their decimal points aligned in your mind. 3.25 + 1.75
  2. Start adding from the rightmost column (the hundredths place). Hundredths place: 5 + 5 = 10. Write down 0 in the hundredths place of the answer, and carry over 1 to the tenths place.
  3. Move to the tenths place. Tenths place: 2 + 7 = 9, plus the carried-over 1 makes 10. Write down 0 in the tenths place of the answer, and carry over 1 to the units place.
  4. Move to the units place. Units place: 3 + 1 = 4, plus the carried-over 1 makes 5. Write down 5 in the units place.
  5. Since both numbers have two decimal places, our answer should also have two decimal places for clarity. So far we have 5.00 from the previous steps.
  6. Final check. 3.25 + 1.75 = (3 + 1) + (0.25 + 0.75) = 4 + 1.00 = 5.00. ANSWER: 5.00

Let's add 3.25 and 1.75 step-by-step.

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