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In this lesson, you will practice working with decimals through guided examples. We will work through problems together, step by step, to build your confidence with decimal place value and comparing decimals.

Key Strategies for Decimal Practice

Line up the decimal points when comparing or adding decimals
Add trailing zeros to make comparison easier (0.5 = 0.50)
Use place value charts to visualize decimal positions
Read decimals aloud using place value names (0.35 = "thirty-five hundredths")

Examples

Work through these examples to see the concepts in action.

Example 1: Identifying Place Value

In the number 3.47, what digit is in the hundredths place?

Solution: The digit 7 is in the hundredths place. Reading from left to right after the decimal: 4 is in the tenths place, 7 is in the hundredths place.

Example 2: Comparing Decimals

Compare 0.6 and 0.58. Which is greater?

Solution: Rewrite 0.6 as 0.60. Now compare: 0.60 > 0.58, so 0.6 is greater.

✏️ Practice

Test your understanding with these practice questions.

Practice Questions

0/4 correct

Question 1

If y = 3x represents a proportional relationship, what is the constant of proportionality?

A 1

B 3

C x

D y

Explanation: In y = kx, the constant of proportionality k is the coefficient of x. Here k = 3.

Question 2

A recipe uses 2 cups of flour for every 3 cups of sugar. If you use 6 cups of flour, how many cups of sugar do you need?

A 4 cups

B 9 cups

C 12 cups

D 8 cups

Explanation: Set up the proportion: 2/3 = 6/x. Cross multiply: 2x = 18, so x = 9 cups.

Question 3

Which equation represents a proportional relationship?

A y = 2x + 1

B y = 5x

C y = x²

D y = 3

Explanation: A proportional relationship has the form y = kx where k is a constant. Only y = 5x fits this form.

Question 4

The table shows x: 2, 4, 6 and y: 8, 16, 24. What is the constant of proportionality?

A 2

B 4

C 6

D 8

Explanation: Divide any y-value by its corresponding x-value: 8÷2 = 4, 16÷4 = 4, 24÷6 = 4. The constant is 4.

Check Your Understanding

Test yourself with these 10 review questions. Click each question to reveal the answer.

Question 1: What is the place value of 5 in the number 2.35?

Answer: Hundredths. The 5 is two places to the right of the decimal point.

Question 2: Which is greater: 0.7 or 0.65?

Answer: 0.7 is greater. Rewrite as 0.70 and compare: 0.70 > 0.65

Question 3: Write 0.4 as an equivalent decimal with two decimal places.

Answer: 0.40. Adding a zero to the right of the last digit does not change the value.

Question 4: In the number 8.19, what digit is in the tenths place?

Answer: 1. The tenths place is the first digit after the decimal point.

Question 5: Order these decimals from least to greatest: 0.3, 0.29, 0.31

Answer: 0.29, 0.3, 0.31. Rewrite 0.3 as 0.30 to compare: 0.29 < 0.30 < 0.31

Question 6: What decimal is shown by 4 tenths and 2 hundredths?

Answer: 0.42. The 4 goes in the tenths place, the 2 goes in the hundredths place.

Question 7: Is 0.50 equal to, greater than, or less than 0.5?

Answer: Equal to. 0.50 and 0.5 represent the same value (five tenths).

Question 8: What is the value of the 6 in 1.67?

Answer: 6 tenths or 0.6. The 6 is in the tenths place.

Question 9: Compare using < or >: 0.09 ___ 0.1

Answer: 0.09 < 0.1. Rewrite 0.1 as 0.10. Then 0.09 < 0.10.

Question 10: Write the decimal for "twenty-three hundredths."

Answer: 0.23. "Hundredths" means two decimal places, and 23 hundredths = 0.23.

Next Steps

Review any concepts that felt challenging
Move on to the next lesson when ready
Return to practice problems periodically for review