Comparing and Ordering Decimals
Semester 4B · Chapter 12 · Lesson 7 · MATH-4B-C12-L07
Before you begin: prerequisite check
Recall: 12.01–12.06. Attempt these questions independently first.
Write 11/20 as a decimal.
Show answer and reasoning
Rename 11/20 in tenths or hundredths (or divide numerator by denominator) to get 0.55.
Write 1/4 as a decimal.
Show answer and reasoning
Rename 1/4 in tenths or hundredths (or divide numerator by denominator) to get 0.25.
Write 1/10 as a decimal.
Show answer and reasoning
Rename 1/10 in tenths or hundredths (or divide numerator by denominator) to get 0.1.
Key vocabulary
- tenth
- one of ten equal parts of a whole
- hundredth
- one of one hundred equal parts
- equivalent decimals
- two notations for the same amount
- midpoint
- exact halfway point between rounding benchmarks
Understand the concept
To compare decimal numbers, first align the ones, tenths, and hundredths. For example, 0.6 = 0.60, and 0.60 is greater than 0.57 because 60 hundredths are more than 57 hundredths. A longer string of digits after the decimal point does not necessarily mean a larger quantity. A number line or grid can confirm the comparison. For ordering three decimals, write them with the same number of decimal places before comparing left to right.
Fully worked examples and immediate checks
Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.
Worked example 1
Insert <, > or =: 0.75 ___ 0.24.
Compare 75 hundredths and 24 hundredths; 0.75 is greater relative to 0.24.
Check 1: try it yourself
Insert <, > or =: 0.46 ___ 0.10.
Show answer and reasoning
Compare 46 hundredths and 10 hundredths; 0.46 is greater relative to 0.10.
Worked example 2
Insert <, > or =: 0.94 ___ 0.96.
Compare 94 hundredths and 96 hundredths; 0.94 is less relative to 0.96.
Check 2: try it yourself
Insert <, > or =: 0.14 ___ 0.14.
Show answer and reasoning
Compare 14 hundredths and 14 hundredths; 0.14 is equal relative to 0.14.
Worked example 3
Insert <, > or =: 0.13 ___ 0.55.
Compare 13 hundredths and 55 hundredths; 0.13 is less relative to 0.55.
Check 3: try it yourself
Insert <, > or =: 0.66 ___ 0.20.
Show answer and reasoning
Compare 66 hundredths and 20 hundredths; 0.66 is greater relative to 0.20.
Guided practice
Insert <, > or =: 0.37 ___ 0.94.
Show answer and reasoning
Compare 37 hundredths and 94 hundredths; 0.37 is less relative to 0.94.
Insert <, > or =: 0.44 ___ 0.54.
Show answer and reasoning
Compare 44 hundredths and 54 hundredths; 0.44 is less relative to 0.54.
Insert <, > or =: 0.85 ___ 0.35.
Show answer and reasoning
Compare 85 hundredths and 35 hundredths; 0.85 is greater relative to 0.35.
Order 0.87, 0.59, and 0.11 from least to greatest.
Show answer and reasoning
Convert all to hundredths and sort the integer counts.
Order 0.18, 0.60, and 0.82 from least to greatest.
Show answer and reasoning
Convert all to hundredths and sort the integer counts.
Independent practice
Insert <, > or =: 0.59 ___ 0.83.
Show answer and reasoning
Compare 59 hundredths and 83 hundredths; 0.59 is less relative to 0.83.
Insert <, > or =: 0.15 ___ 0.49.
Show answer and reasoning
Compare 15 hundredths and 49 hundredths; 0.15 is less relative to 0.49.
Insert <, > or =: 0.71 ___ 0.91.
Show answer and reasoning
Compare 71 hundredths and 91 hundredths; 0.71 is less relative to 0.91.
Order 0.89, 0.22, and 0.17 from least to greatest.
Show answer and reasoning
Convert all to hundredths and sort the integer counts.
Order 0.95, 0.45, and 0.80 from least to greatest.
Show answer and reasoning
Convert all to hundredths and sort the integer counts.
Insert <, > or =: 0.85 ___ 0.62.
Show answer and reasoning
Compare 85 hundredths and 62 hundredths; 0.85 is greater relative to 0.62.
Insert <, > or =: 0.86 ___ 0.33.
Show answer and reasoning
Compare 86 hundredths and 33 hundredths; 0.86 is greater relative to 0.33.
Insert <, > or =: 0.73 ___ 0.56.
Show answer and reasoning
Compare 73 hundredths and 56 hundredths; 0.73 is greater relative to 0.56.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Insert <, > or =: 0.41 ___ 0.87. Explain how place value or a model can check your result.
Show answer and reasoning
Compare 41 hundredths and 87 hundredths; 0.41 is less relative to 0.87. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “0.45 is greater than 0.5 because 45 is greater than 5.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: 0.5 = 0.50, and 45 hundredths are fewer than 50 hundredths. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Insert <, > or =: 0.98 ___ 0.26.
Show answer and reasoning
Compare 98 hundredths and 26 hundredths; 0.98 is greater relative to 0.26.
Insert <, > or =: 0.41 ___ 0.71.
Show answer and reasoning
Compare 41 hundredths and 71 hundredths; 0.41 is less relative to 0.71.
Insert <, > or =: 0.86 ___ 0.73.
Show answer and reasoning
Compare 86 hundredths and 73 hundredths; 0.86 is greater relative to 0.73.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.