Lesson 4 of 8 · Grades 4 to 5
Comparing decimals
Comparing decimals means deciding which number is larger. A longer decimal is not automatically bigger: 0.45 is less than 0.5. This lesson gives you a place-by-place method that always works, and shows why a zero at the end of a decimal changes nothing.
Compare place by place from the left
Comparing decimals means deciding which number is larger. A longer decimal is not automatically bigger. The decimal 0.45 has more digits than 0.5, yet 0.45 is smaller. The safe method is to compare one place at a time, starting from the left.
Compare 0.45 and 0.5. The whole parts are both 0, so they tie. Look at the tenths place: 4 against 5. Five tenths is more than four tenths, so 0.5 is larger. There is no need to look at the hundredths at all.
The zero at the end
The decimal 0.5 and the decimal 0.50 name the same amount: five tenths is fifty hundredths. Adding a zero at the end of a decimal does not change its value. That trick is useful for comparing. Write both numbers with the same number of decimal places, then compare the columns like whole numbers: 0.45 against 0.50, and 45 is less than 50. When a comparison looks close, rewriting both numbers in the same place is the safest first step.
Longer is not larger
The trap works both ways. The number 1.7 looks shorter than 1.65, but 1.7 is larger, because 1.7 is 1.70 and 70 hundredths is more than 65 hundredths. To compare them, write 1.7 as 1.70 and line up the places.
Ordering three decimals
To order 0.7, 0.68 and 0.8, write all three in hundredths: 0.70, 0.68 and 0.80. Then compare the tenths first, and use the hundredths to break a tie. The tenths digits are 7, 6 and 8, so 0.68 comes first and 0.8 comes last. The order from smallest to largest is 0.68, 0.7, 0.8.
A number line is another way to check an order. Numbers grow as you move to the right, so the point further right is always the larger number. When two decimals look almost the same, place them on a tenths or hundredths line and read the order straight off the picture.
Watch out for this
Compare 0.09 with 0.1 and the answer surprises many people. The number 0.09 is only 9 hundredths, while 0.1 is 10 hundredths, so 0.1 is larger. More digits does not mean more value. Write both decimals in the same place before you compare.
Worked example
Order 0.7, 0.68 and 0.8 from smallest to largest, using hundredths.
Step 1: write all three with two decimal places: 0.70, 0.68 and 0.80.
Step 2: compare the tenths digits first. They are 7, 6 and 8, so 0.68 has the smallest tenths.
Step 3: the other two both have 7 and 8 tenths, and 70 is less than 80.
Step 4: put them in order: 0.68, 0.70, 0.80.
Answer: 0.68, 0.7, 0.8.
Remember
- Compare the whole part first, then tenths, then hundredths.
- Stop at the first place where the digits differ.
- A zero at the end of a decimal changes nothing: 0.5 = 0.50.
- On a number line, the number further right is always larger.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
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Which is larger: 0.6 or 0.58?
Show answer
0.6. Write it as 0.60, and 60 hundredths is more than 58 hundredths.
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Which is smaller: 3.2 or 3.02?
Show answer
3.02. Write 3.2 as 3.20, and 3.02 is less than 3.20.
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Write 0.7 with two decimal places.
Show answer
0.70. The extra zero does not change the value.
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Order from smallest to largest: 0.5, 0.45, 0.55.
Show answer
0.45, 0.5, 0.55.
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Which decimal is between 0.3 and 0.4: 0.35, 0.43 or 0.29?
Show answer
0.35. It sits between 0.30 and 0.40.
Puzzle · Mystery decimal
Puzzle time
I am a decimal with two decimal places. I am more than 0.6 and less than 0.7. My hundredths digit is 5 less than my tenths digit. What number am I?
Show a hint
The tenths digit must be 6, because the number is between 0.6 and 0.7. Then subtract 5.
Show the answer
Answer: 0.61. The tenths digit is 6, and 6 - 5 = 1, so the number is 0.61.