Concept 5 of 8
Decimal Place Value
Today's big idea
Each decimal place is 10× smaller: tenths, hundredths, thousandths.
Longer is not larger: 0.4 beats 0.38.
How it works
👀 What's going on?
A stopwatch reads 3.547 seconds. Those three digits after the point are not a whole number at all. Each one is ten times smaller than the digit before it.
💡 Here's the trick
Look at the chart above. The places to the right of the point are tenths, then hundredths, then thousandths. A digit is worth itself times the place it sits in.
🪄 How to do it
- 1.Name the places in the chart above from left to right.
- 2.Multiply each digit by the size of its place.
- 3.To compare, pad both numbers with zeros and read left to right.
✍️ Try it
In 6.502, what is the 5 worth? Then say which is larger, 0.38 or 0.4.
The 5 sits in the tenths place, so it is worth 0.5. Padding turns the pair into 0.38 and 0.40, so 0.4 is larger.
⚠️ Watch out
You might be thinking a longer decimal must be the bigger one. Digits are weighed, not counted. 0.4 beats 0.38 because 4 tenths beats 3 tenths, whatever follows.
🌟 Why this matters
Race times, price tags and medicine doses all run to two or three places. Reading the right place is the whole of the meaning.
Exam tip: Pad every decimal to the same length before you compare or order them.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“What is the value of the 7 in 5.073?”
- 1
Count places after the point
0 → tenths · 7 → hundredths · 3 → thousandths. 🎯
- 2
Find the 7
The 7 sits in the hundredths place.
- 3
Value of that place
Hundredths place is worth 1/100 each.
- 4
Answer ✓
The 7 is worth 7 hundredths = 0.07
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
1st place after the dot = tenths · 2nd = hundredths · 3rd = thousandths.
DECIMAL · ROUND 1 OF 3
8.36 — focus on the 6
Quick check
✅ VERIFICATION
Which number has a 6 in the hundredths place?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Add & Subtract Decimals
Line up the decimal point.