Lesson Guide
Explanation
Here is the trap that catches nearly everyone. Which is bigger, 0.7 or 0.65? It is tempting to say 0.65 because 65 looks bigger than 7. But look at the bars: 0.7 covers more. The reason is that after the decimal point you are not reading a whole number any more — you are reading columns. Seven tenths beats six tenths, and what comes after cannot rescue it. More digits does not mean a bigger number.
Your Turn
Which is bigger, 0.4 or 0.39? Check: 0.4, because 4 tenths beats 3 tenths.
Watch Out
Never compare the digits after the point as if they were a whole number. 0.65 is not 'sixty-five'.
Explanation
The reliable method is to compare column by column, starting from the left. For 3.64 against 3.61: the ones are both 3, a tie. The tenths are both 6, a tie. The hundredths are 4 and 1, so 3.64 wins. The important part is that the FIRST column that differs decides the whole thing — once you find it you can stop, because nothing further right is big enough to overturn it.
Your Turn
Compare 5.28 and 5.31 column by column. Check: ones tie, then 3 tenths beats 2 tenths, so 5.31 is bigger.
Watch Out
Start at the LEFT, not the right. The biggest columns decide first.
Explanation
There is a trick that makes this much easier. Give both numbers the same number of decimal places by adding zeros on the end. So 0.7 becomes 0.70, and now you are comparing 70 hundredths with 65 hundredths, which is obvious. Adding a zero on the END of a decimal changes nothing at all — seven tenths and seventy hundredths are the same amount. That is very different from a zero straight after the point, which changes everything.
Your Turn
Even up 0.5 and 0.48, then compare. Check: 0.50 against 0.48, so 0.5 is bigger.
Watch Out
A zero on the END is harmless; a zero straight AFTER the point is not. 0.70 = 0.7, but 0.07 does not.
Explanation
To put several decimals in order, even them all up first so every one has the same number of places, then read down the columns. Writing them under each other with the decimal points lined up makes it almost automatic. Here 2.5, 2.35, 2.09 and 2.4 become 2.50, 2.35, 2.09 and 2.40, and the order is clear: 2.09, 2.35, 2.4, 2.5. Notice 2.09 is smallest even though it has the biggest-looking digits after the point.
Your Turn
Order 1.7, 1.07, 1.75 from smallest. Check: even up to 1.70, 1.07, 1.75, giving 1.07, 1.7, 1.75.
Watch Out
Line the decimal POINTS up, not the ends of the numbers. That is what keeps the columns honest.
Explanation
This shows up constantly in real life. Which price is cheaper, $3.05 or $3.50? Even them up — they already are — and compare: 0 tenths against 5 tenths, so $3.05 is cheaper by 45 cents. And in a race, 12.35 seconds beats 12.4 seconds, because a smaller time means faster. That last one is worth pausing on: the smaller number wins. Always read what the question is actually asking, because bigger and better are not always the same thing.
Your Turn
A jump of 3.5 m or 3.45 m — which is longer? Check: 3.5 m, since 3.50 beats 3.45.
Watch Out
For times and prices, smaller is usually better. For jumps and scores, bigger is. Read the question.
📌 Key Points — this lesson in a nutshell
- More digits does not mean a bigger number: 0.7 beats 0.65.
- Compare column by column from the left. The first column that differs decides it.
- Even the places up with zeros on the end — that changes nothing.
- Line up the decimal points when ordering several.
- In races and prices the smaller number wins. Read the question.
Step 1: Introduction
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