Tenths, hundredths and thousandths: what each place is worth, how to read a decimal aloud, and where it sits on a number line. Comparing and ordering without falling for ‘longer is bigger,’ rounding to a tenth or a whole, and adding and subtracting with the points lined up. Then multiplying and dividing decimals, moving the point for tens and hundreds, and money problems that use all of it. Study cards, hints, a practice quiz at three levels, and four workshop activities that check themselves.
Two amounts of the same bar. The top one is clearly a little bigger.
The place names the fraction: tenths, then hundredths. Pad them to the same number of places and then compare like whole numbers — the length of the number tells you nothing.
Two things people get wrong
⚠️People often think…
0.35 is bigger than 0.4, because 35 is bigger than 4.
More digits does not mean more. 0.4 is four tenths; 0.35 is thirty-five hundredths, which is only three and a half tenths. Pad the short one — 0.40 against 0.35 — and it settles instantly.
Pad with zeros until both are the same length.
⚠️People often think…
To add 4.6 + 2.75, line up the right-hand ends.
Line up the decimal POINTS, so tenths sit over tenths. Lining up the ends puts the 6 tenths under the 5 hundredths and turns the problem into 46 + 275, which is not remotely the same question.
Points in a column. Pad the short one.
Pad it, line it up, count the places
1Watch one
Which is bigger: 0.4 or 0.35?
They have different numbers of places.
Pad the short one: 0.40.
Now compare 40 and 35.
0.4 is bigger.
2Do one with me
4.6 + 2.75.
Before adding, line up the
Pad 4.6 so it has two places:
Now add:
💬One sentence, then you move on
Why do you line up the decimal points instead of the right-hand ends?
3Try one
0.6 × 0.3 = ?
I want a hint first
6 × 3 = 18. One decimal place in each number means two places in the answer.
Where this goes
Where this lives
Every price tag, a gas pump, a batting average, and the moment somebody tells you $0.9 and means ninety cents.
What this feeds
Next unit is measurement — area, perimeter and volume, where the units do the checking for you.
Find a price near you and say how many hundredths it is.
One card at a time — tap “Show me” to check yourself, then Next. Start at Foundation; when those feel easy, climb.
Helpful Hints
⚖️ Comparing and ordering decimals — the routine
Line up the decimal points in a column → add zeros at the END until every number has the same number of places → read the digits after the point as whole numbers and compare → the biggest whole number is the biggest decimal. 0.5, 0.45, 0.405 → 0.500, 0.450, 0.405 → 500, 450, 405 → 0.5 is greatest, 0.405 is least.
Line up, pad, compare left to right.
💡 The whole topic in one idea
A decimal is a fraction whose bottom is 10, 100 or 1000 — and the PLACE tells you which. One digit after the point: tenths. Two: hundredths. Three: thousandths. Every rule in this room — comparing, rounding, adding, multiplying — is just place value working past the decimal point, the same way it works before it.
The place names the fraction.
⚠️ Traps the test loves
Thinking longer is bigger: 0.35 > 0.4 because 35 > 4. Pad first: 0.40 vs 0.35.
Lining up the right-hand ends instead of the decimal points: 4.6 + 2.75 as 46 + 275.
Rounding with the wrong digit: 6.49 → 7 because of the 9. Only the digit right next door decides, and it is 4.
Adding a zero to multiply by 10: 0.47 × 10 = 0.470. Zeros at the end do nothing; the POINT moves.
Forgetting to count decimal places when multiplying: 0.6 × 0.3 = 1.8. One place plus one place is two places: 0.18.
Losing the point when dividing: 6.4 ÷ 8 = 8. Estimate first — 6.4 shared by 8 must be less than 1.
🏷️ Places after the point — the chart
Place
Fraction
Decimal
Money
Tenths — 1st place
1/10
0.1
a dime
Hundredths — 2nd place
1/100
0.01
a penny
Thousandths — 3rd place
1/1000
0.001
a tenth of a penny
Half
1/2 = 5/10
0.5
50 cents
Quarter
1/4 = 25/100
0.25
a quarter
Three quarters
3/4 = 75/100
0.75
75 cents
🎯 How the test will ask
A decimal — “what is the value of the 7?” Name the place, then the amount: 7 hundredths = 0.07.
Three or four decimals — “order them” or “which is greatest?” Pad with zeros, then compare.
A number line with tenths — “what number is at the arrow?” Count the jumps from 0.
“Round to the nearest tenth / whole number.” Find the place, look one to the right, decide.
A money story — add, subtract or multiply prices. Points in a column; cents with two digits.
“× 10” or “÷ 100” — the point moves, one place per zero.
A product like 0.4 × 0.6 — multiply, then count the decimal places in both factors.
✅ Before the test, can you…
Write 3/10, 25/100 and 405/1000 as decimals, and read each one aloud?
Find 0.4 and 0.75 on a number line from 0 to 1?
Put 0.5, 0.45 and 0.405 in order and explain why 0.5 is greatest?
Round 3.47 to the nearest tenth and 6.49 to the nearest whole?
Add 2.35 + 1.4 and subtract 5 − 1.25 with the points lined up?
Multiply 0.3 × 0.2 and divide 4.8 ÷ 4, and put the point in the right spot?
Say what happens to 2.5 when you multiply by 100 or divide by 10?
Pick your level
Look back at anything you missed — the hint that appeared is exactly what to reread tonight.
How sure did you feel?
Workshop
Work like a mathematician: place decimals on a number line, line them up from least to greatest, decide which way each one rounds, then graph a week of lunch money to the quarter. Every activity checks itself, and hints are free.
Your practice never leaves this device. There is no account and no sign-in. Your work is saved in this browser only, and you can erase it whenever you want.
Your practice record — saved on this device
This is your record of the module on screen — it stays here and goes nowhere. Independent means you got it right on the first tap; supported means you got it after the explain-and-retry, or marked ‘I had it’ on a revealed answer. Both count, and neither is a grade. If your teacher asks, copy the row or show them this screen.
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