Free printable decimal chart
Grades 4–6Tenths, hundredths and thousandths, how decimals line up against fractions and percents, and how to tell which of two is bigger. Print it for the wall, or put two decimals into the live comparison below and see them measured against each other.
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Which decimal is bigger?
Type two decimals and they are drawn as lengths on the same scale from 0 to 1. Underneath, each one is written as a fraction and a percent, and the note explains which is larger and why.
Start with the pair already loaded: 0.45 and 0.7. A great many children will say 0.45 is bigger, because it has more digits, and that is a perfectly sensible thing to believe if you have spent five years learning that longer numbers are larger. The bars settle it in about a second.
Then try 0.5 against 0.50. The bars are identical, because they are the same amount — a zero on the end of a decimal adds nothing. That fact is the reason children can compare decimals at all: pad the shorter one with zeros and both have the same number of places.
- A as a fraction and a percent
- 45/100 = 9/20 = 45%
- B as a fraction and a percent
- 7/10 = 7/10 = 70%
Compare the tenths first: 7 beats 4, so 0.7 is bigger. The number of digits does not decide it — the place values do.
How to use this decimals chart at home
Start with money, because they already know it. A child who cannot say whether 0.45 is bigger than 0.7 can usually tell you instantly that 45 cents is less than 70 cents. Same numbers, same question, and the money version is already solid. Building from that is far quicker than starting from scratch.
Insist on the long reading for a while. Not three point four five but three and forty-five hundredths. It is slower and it makes the value audible, and children who only ever say point four five tend to treat the digits as a separate little number rather than as parts of a whole.
Use the comparison tool above whenever an answer looks odd. Decimal errors are almost always about size rather than arithmetic, and seeing two lengths on the same scale settles arguments faster than any explanation.
Why more digits does not mean bigger
For years, longer numbers have been larger. 100 beats 99, 1,000 beats 999, and the rule has never once let a child down. Then decimals arrive and it breaks immediately: 0.45 has more digits than 0.7 and is smaller.
What actually decides it is the leftmost column where the two differ. Tenths outrank hundredths no matter how many hundredths there are, in exactly the same way that hundreds outrank tens on the other side of the point. It is the same system, running in the same direction.
The reliable fix is padding with zeros. Write 0.7 as 0.70 and both numbers have two places, at which point the old rule works again — 70 beats 45. Teaching that as a habit rather than a trick gives children something they can use every time.
Decimals, fractions and percents are one idea
0.45 is forty-five hundredths, which is 45/100, which is 45%. Three notations, one amount, and the live tool above shows all three moving together.
Percent is the easiest of the three, and it is worth using as a bridge. Children have a strong feel for what 70% means long before they have any feel for 0.7, so converting to a percent is often the fastest way to make a decimal mean something.
The tenths and hundredths that decimals use are also why they convert so cleanly. Any decimal is already a fraction with a denominator of 10, 100 or 1000 — the point is a compact way of writing exactly that, and nothing more mysterious.
Where decimals usually go wrong
Judging by length. Believing 0.45 beats 0.7, or that 0.125 beats 0.9. The commonest decimal error there is, and the bars above are the fastest cure.
Losing the point in addition. Adding 3.4 and 12.75 with the digits pushed to the right rather than lined up at the point. Whole-number addition can be right-aligned safely; decimal addition cannot, and children carry the old habit across.
Confusing a trailing zero with a middle one. Believing 0.5, 0.05 and 0.50 are interchangeable. Two of those are equal and one is a tenth of the others, and the difference is entirely about whether the zero is holding a place open.
Reading the digits as a whole number. Saying 3.45 is bigger than 3.5 because forty-five is bigger than five. The digits after the point are not a number in their own right — they are columns, and each has its own value.
After the chart goes up
A chart explains the idea but gives a child nothing to do. These do the rest.
- decimals at Mathify Kids — every topic in this area, sorted by grade.
- comparing decimals worksheets — printable practice.
- rounding decimals worksheets — the next step once this is solid.
- add subtract decimals worksheets — more practice in the same area.
Everything at this level: Grade 4 math · Grade 5 math · Grade 6 math
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Questions parents ask
Which is bigger, 0.45 or 0.7?
0.7 is bigger. Compare the tenths first: 7 tenths beats 4 tenths, and nothing in the hundredths column can make up the gap. The number of digits after the point does not decide the size — the place values do. This is the single most common decimal misconception, and it comes from a whole-number rule that used to work.
How do you compare two decimals?
Line them up at the decimal point and compare one column at a time from the left, exactly as you would with whole numbers. Pad the shorter one with zeros so both have the same number of places — 0.7 becomes 0.70 — and the comparison becomes obvious. The first column where they differ decides it.
Is 0.5 the same as 0.50?
Yes. A zero on the end of a decimal adds nothing, because it is saying there are no hundredths, which was already true. This is different from a zero in the middle: 0.05 is a tenth of 0.5, because there the zero is holding a place open.
What is each place after the decimal point worth?
The first is tenths, worth 0.1 each. The second is hundredths at 0.01, the third thousandths at 0.001. Each column is worth a tenth of the one to its left, which is exactly the pattern the whole-number columns follow going the other way — it is one continuous system, not two.
How do you read a decimal out loud?
Say the whole number, then and, then the digits after the point followed by the name of the last place. So 3.45 is three and forty-five hundredths. Reading it as three point four five is fine in conversation, but the long version is what makes the value audible, and it is worth insisting on while a child is learning.
What grade is this decimals chart for?
Grades 4 to 6. Tenths and hundredths usually arrive in Grade 4, comparing and rounding in Grade 5, and operations with decimals by Grade 6. Money means children handle decimals informally long before any of this.
Is this decimals chart free to print?
Yes. Open it full size and print as many copies as you need for home or a classroom, with no account and no watermark. Reselling it or re-hosting the file elsewhere is not allowed — link to this page instead.