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➗ Math · Numbers and Algebra · Lesson 4 of 8 · 5 min

Comparing and ordering fractions, decimals and negatives

📏 Is 0.6 bigger than 0.58? Is −1/2 bigger than −3/4? These quick comparisons trip up more test takers than hard algebra does.

💡 Key idea

Convert everything to decimals, line up the places, and remember that for negatives, closer to zero is greater.

🧠 The idea

To compare numbers written in different forms, CONVERT them all to decimals, then compare digit by digit from the left. Padding with zeros helps: 0.6 = 0.60, which is greater than 0.58. A longer decimal is not automatically bigger; 0.125 is less than 0.2. To compare two fractions, you can also use a COMMON DENOMINATOR or CROSS-MULTIPLY: for 5/8 and 3/5, compare 5 × 5 = 25 with 8 × 3 = 24, so 5/8 is larger. On the NUMBER LINE, numbers grow to the right. That means negatives flip your intuition: −0.5 is greater than −0.75 because it sits closer to zero, and any negative is less than any positive. ASCENDING order runs least to greatest; DESCENDING runs greatest to least. Read the question twice to see which one it wants.

✏️ Worked example

Order from least to greatest: 2/3, 0.6, 65%, 5/8.
Step 1: Convert: 2/3 ≈ 0.667, 0.6 = 0.600, 65% = 0.650, 5/8 = 0.625.
Step 2: Compare the decimals: 0.600 < 0.625 < 0.650 < 0.667.
Step 3: Translate back to the original forms.
Answer: 0.6, 5/8, 65%, 2/3.

📌 Takeaways

  • Turn every number into a decimal, then add zeros so they have the same length.
  • Cross-multiply to compare two fractions quickly.
  • On the number line, farther right is greater, even for negatives.

✅ Check yourself

Question 1 of 3

Which number is greatest?

  1. 0.09
  2. 0.1
  3. 0.089
  4. 0.0999
Show the answer and rationale

Answer: B

Pad to four places: 0.0900, 0.1000, 0.0890, 0.0999. The value 0.1 has a 1 in the tenths place, and the others have 0 there, so it is the greatest. The value 0.0999 looks bigger because it has more digits, but length does not decide size.

Question 2 of 3

Which list is in order from least to greatest?

  1. 1, 0, −2, −5
  2. 0, −2, −5, 1
  3. −5, −2, 0, 1
  4. −2, −5, 0, 1
Show the answer and rationale

Answer: C

On the number line −5 is farthest left, then −2, then 0, then 1. The list starting −2, −5 treats −5 as bigger because 5 is bigger than 2, and the list starting with 1 is in descending order.

Question 3 of 3

Which statement is true?

  1. 5/6 < 0.8
  2. 5/8 > 0.6
  3. 3/7 > 1/2
  4. 4/9 > 0.45
Show the answer and rationale

Answer: B

5/8 = 0.625, which is greater than 0.600. The others are false: 3/7 ≈ 0.429 is less than 1/2, 4/9 ≈ 0.444 is just under 0.450, and 5/6 ≈ 0.833 is greater than 0.8, not less.

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