Place Value Decimals

Grade 5 · decimals · 90 practice problems · read aloud

🔊 Listen to this explanation

Place Value with Decimals

🔍 What is Decimal Place Value?

Decimal place value helps us understand numbers that are less than one whole. We use a decimal point (.) to separate the whole numbers from the parts of a whole. This is super useful for measuring things like length, weight, and money!

📝 Step-by-Step Guide

Let's break down the place values to the right of the decimal point:

  1. Tenths (0.1): The first digit after the decimal. It means 1 out of 10 equal parts.
  2. Hundredths (0.01): The second digit after the decimal. It means 1 out of 100 equal parts.
  3. Thousandths (0.001): The third digit after the decimal. It means 1 out of 1000 equal parts.

✨ Visual Examples

Example 1: The number 4.73

4 . 7   3
Ones   Tenths   Hundredths

This means: 4 ones + 7 tenths + 3 hundredths.
We say: "Four and seventy-three hundredths."

Example 2: The number 0.508

0 . 5   0   8
Ones   Tenths   Hundredths   Thousandths

This means: 0 ones + 5 tenths + 0 hundredths + 8 thousandths.
We say: "Five hundred eight thousandths."

⚠️ Common Mistakes

Forgetting the "And": Always say "and" for the decimal point. 3.4 is "three and four tenths," not "three point four."

Misreading Zero: In a number like 2.05, the zero is a placeholder. It's "two and five hundredths," NOT "two and five tenths."

Confusing Place Values: Remember that the tenths place is ten times bigger than the hundredths place!

💡 Tips & Tricks

Money Connection: Think of decimals as money! $1.25 has 1 whole dollar, 2 dimes (tenths), and 5 pennies (hundredths).

Place Value Chart: Draw a chart to organize the digits. It's a great visual tool!

Thousandths Trick: The word "thousandths" has the most letters, so it's the smallest place value (farthest from the decimal).

🎯 Practice Suggestions

  • Write down different decimal numbers and say them out loud.
  • Use a deck of cards to create random decimals and identify the value of the underlined digit.
  • Find decimals in real life! Look at food nutrition labels, gas prices, or a ruler.

Practice problems

6 of the 90, worked through step by step — try them before opening the answer.

1 0.375 × 0.8 = ?

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 the product.

Show the answer

Answer: 0.3

  1. Write both decimals as fractions. 0.375 = 375/1000 0.8 = 8/10
  2. Multiply the fractions. (375/1000) × (8/10) = (375 × 8) / (1000 × 10)
  3. Calculate the numerator and denominator. Numerator: 375 × 8 375 × 8 = 3000 Denominator: 1000 × 10 = 10000 So we have: 3000/10000
  4. Simplify the fraction. Divide numerator and denominator by 100: 3000 ÷ 100 = 30 10000 ÷ 100 = 100 So 3000/10000 = 30/100
  5. Simplify further. 30/100 = 3/10
  6. Convert back to decimal. 3/10 = 0.3 Therefore, 0.375 × 0.8 = 0.3

Let's solve 0.375 × 0.8 step by step.

2 0.456 × 0.3 = ?

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

Show the answer

Answer: 0.1368

  1. Multiply the numbers as if they were whole numbers: 456 × 3 = 1368.
  2. Count the total number of decimal places in the original factors. 0.456 has 3 decimal places and 0.3 has 1 decimal place, so the total is 3 + 1 = 4 decimal places.
  3. Place the decimal point in the product (1368) so that it has 4 decimal places. This gives 0.1368.

The answer is 0.1368.

3 0.456 × 0.25 = ?

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

Show the answer

Answer: 0.114

  1. Multiply the numbers as if they were whole numbers: 456 × 25
  2. 456 × 20 = 9120
  3. 456 × 5 = 2280
  4. Add the partial products: 9120 + 2280 = 11400
  5. Count the decimal places: 0.456 has 3 decimal places, 0.25 has 2 decimal places, so total decimal places = 3 + 2 = 5
  6. Place the decimal point in 11400 to get 5 decimal places: 0.11400
  7. Remove unnecessary zeros: 0.114

The answer is 0.114.

4 0.456 × 0.75 = ?

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

Show the answer

Answer: 0.342

  1. Multiply the numbers as if they were whole numbers: 456 × 75.
  2. Calculate 456 × 75 = 456 × (70 + 5) = (456 × 70) + (456 × 5) = 31920 + 2280 = 34200.
  3. Count the total decimal places in the original factors: 0.456 has 3 decimal places, and 0.75 has 2 decimal places, so the total is 3 + 2 = 5 decimal places.
  4. Place the decimal point in the product (34200) so that it has 5 decimal places: 0.34200.
  5. Simplify by removing the trailing zeros: 0.34200 becomes 0.342.

The answer is 0.342.

5 0.375 + 0.624 = ?

Hint: When adding decimals, align the decimal points and add each place value column from right to left, carrying over when necessary.

Show the answer

Answer: 0.999

  1. Write the numbers aligned by their decimal points in your mind: 0.375 + 0.624
  2. Add the digits in the thousandths place (third decimal place): 5 (thousandths) + 4 (thousandths) = 9 thousandths. So, the thousandths place of the result is 9.
  3. Add the digits in the hundredths place (second decimal place): 7 (hundredths) + 2 (hundredths) = 9 hundredths. So, the hundredths place of the result is 9.
  4. Add the digits in the tenths place (first decimal place): 3 (tenths) + 6 (tenths) = 9 tenths. So, the tenths place of the result is 9.
  5. Add the whole number parts: 0 + 0 = 0.
  6. Combine the whole number part and decimal part: 0 . 9 9 9 So, 0.375 + 0.624 = 0.999. We can verify by converting to fractions: 0.375 = 375/1000 = 3/8 0.624 = 624/1000 = 78/125 But adding directly as decimals is simpler here. Final answer: 0.999

Let's add 0.375 and 0.624 step by step.

6 4.375 + 2.618 = ?

Hint: When adding decimals, make sure to align the decimal points and add each place value carefully from right to left.

Show the answer

Answer: 6.993

  1. Write the numbers one under the other, aligning the decimal points. 4.375 + 2.618 ---------
  2. Start adding from the rightmost digit (thousandths place). Thousandths place: 5 + 8 = 13 Write down 3 in the thousandths place, carry over 1 to the hundredths place.
  3. Add the hundredths place, including the carryover. Hundredths place: 7 + 1 + 1 (carry) = 9 Write down 9 in the hundredths place.
  4. Add the tenths place. Tenths place: 3 + 6 = 9 Write down 9 in the tenths place.
  5. Add the units place. Units place: 4 + 2 = 6 Write down 6 in the units place.
  6. Combine all digits, placing the decimal point in the same column. Result: 6.993 Therefore, 4.375 + 2.618 = 6.993

Let's add 4.375 and 2.618 step by step.

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