Moving one place left multiplies a digit by 10. Moving one place right divides it by 10.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
An example
In 4,440 the first 4 is worth 4,000, the next 400, the next 40. Each is a tenth of the one before.
The pattern does not stop
One place right of the ones is tenths. One more is hundredths. Nothing new is happening.
Why this matters
Every rule about decimals comes from this one pattern. Nothing about the point is arbitrary.
Step 2: Try It Yourself
Tap and try it out.
Hundreds
4
Tens
4
Ones
4
4 hundreds, 4 tens and 4 ones is 444.
Step 3: In Real Life
An odometer
An odometer reads 12,345.6. The 6 is a tenth of a mile. The 5 is a whole mile, ten times bigger. Each place to the left is ten times the last. Each place to the right is a tenth of it.
Step 4: Watch an Example
One step at a time.
Watch Ana Compare Two Digits
Ana looks at the two 6s in 660.
- Step 1
The left 6 sits in the hundreds place, so it is worth 600.
Step 5: Your Turn
Practice makes it stick.
The Two Digits
Problem 1 of 2
In 3,300, how many times bigger is the left 3 than the right one?
times
The Other Way
Problem 2 of 2
700 divided by 10 gives what?
Left and Right
1 of 4
80 × 10 = ?
2 of 4
900 ÷ 10 = ?
3 of 4
In 5,500, what is the left 5 worth?
4 of 4
What is one place right of the ones called?
Find It on the Chart
Build it, then check.
Find 120 on the chart.
Step 6: Quick Check
Show what you know.
Question 1 of 2
600 ÷ 10 = ?
Question 2 of 2
What does moving a digit one place left do to its value?
What You Learned
- Each place is ten times the place to its right.
- Each place is one tenth of the place to its left.
- The pattern carries straight on past the decimal point.
For the grown-up
The pattern that built whole numbers continues to the right of the decimal point without changing. Each place is a tenth of the one before, which is the same rule read the other way.
Watch for the decimal point being treated as a separator between two whole numbers. It is a marker for where the ones place ends, nothing more.
Say the place names aloud: three and four tenths, not three point four. The words carry the structure that the notation hides.
The rule runs both ways forever — Move one place left and the value multiplies by ten. Move one place right and it divides by ten. That single rule generates every place in the system, from millions down through thousandths and beyond. The decimal point is not where the rule changes — it is only a marker showing where the ones place sits.
The pattern is symmetrical about the ones, not the point — Many people expect a "oneths" place to mirror the ones. There is none. The places run hundreds, tens, ones, tenths, hundredths — with ones at the center and the point immediately to its right. Getting this straight prevents a whole family of place-naming errors.
The same digit at different scales — In 4.44 the three 4s are worth 4, 0.4 and 0.04. Each is a tenth of the one to its left. Being able to say what any digit in any number is worth, instantly, is the foundation everything in this chapter rests on.
Why this earns a whole lesson — Every decimal operation this year is justified by this rule. Multiplying by ten shifts digits left; dividing shifts them right; lining up decimal points aligns like units. If the rule is solid, the rest of the year is bookkeeping. If it is shaky, every procedure becomes a separate thing to memorize.
Left is ten times, right is a tenth — Look at 555.5. Each step left multiplies by 10: 5 ones, 5 tens, 5 hundreds. Each step right divides by 10: 5 ones, then 5 tenths. The point does not separate two kinds of number. It just marks where the ones stop.