Moving one place left multiplies a digit by 10. Moving one place right divides it by 10.
Step 1: Picture It
Start with something you already know.
Bills and coins
- Ten one-dollar bills trade for one ten-dollar bill.
- Ten dimes trade for one dollar.
- Ten pennies trade for one dime.
Each step up is ten times; each step down is one tenth.
Where it stops: coins end at pennies, but places never end.
Step 2: Let's Learn
Read it, or press Listen and follow the words.
Try it first
In 330, the left 3 is worth 300. What is the right 3 worth?
Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.
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 3: Try It Yourself
Tap and try it out.
Hundreds
4
Tens
4
Ones
4
4 hundreds, 4 tens and 4 ones is 444.
Step 4: 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 5: Watch an Example
One step at a time.
Watch Ana Compare Two Digits
Ana looks at the two 8s in 8,800.
- Step 1
The left 8 sits in the thousands place. It is worth 8,000.
Watch Leo Multiply by Ten
Leo works out 2.7 × 10. He starts, and you finish.
- Step 1
Times 10 moves every digit one place left. The 2 is in the ones. It moves to the tens.
Step 6: Your Turn
Practice makes it stick.
The Bead Box
Problem 1 of 12
A jar holds 250 beads. A box holds 10 jars. How many beads are in the box?
beads
Sharing the Prize
Problem 2 of 12
Ten friends share $8 equally. How much does each friend get?
dollars
Left and Right
Say which way the digit moves. Then answer.
Problem 3 of 12
20 × 10 = ?
Problem 4 of 12
400 ÷ 10 = ?
Problem 5 of 12
In 6.6, what is the right 6 worth?
Find the Mistake
One line on each page is a slip. Find it, then fix it.
Problem 6 of 12
Dev works out 50 × 10. One line is a slip. Which?
Dev's answer for 50 × 10
- 150 × 10
- 25 tens × 10 = 5 thousands
- Answer50 × 10 = 5,000
Problem 7 of 12
What should Dev's answer be?
Problem 8 of 12
Maya works out 0.6 × 10. One line is a slip. Which?
Maya's answer for 0.6 × 10
- 10.6 × 10
- 2A zero on the end: 0.60
- Answer0.6 × 10 = 0.60
Problem 9 of 12
What is 0.6 × 10?
Which Way?
Pick the way that starts right.
Problem 10 of 12
Sam needs 35 ÷ 10. Which way?
Problem 11 of 12
Priya wants one tenth of 70. Which way?
Build the Number
Build it, then check.
Problem 12 of 12
One 9 is worth 900. The other 9 is worth 90. Build the number.
Nothing.
Hundreds
0
Tens
0
Ones
0
0 hundreds, 0 tens and 0 ones is 0.
Step 7: 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?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 2
A three-digit number uses only the digits 1, 1 and 0. One 1 is worth ten times the other. What is the number?
Stretch 2 of 2
In 30.3, the left 3 is how many times the right 3?
times
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 slip this lesson targets is "times ten means add a zero". It works for whole numbers and fails at the first decimal: 0.6 × 10 is not 0.60. Ask which place the digit moves to, tenths to ones, rather than what gets added. Dev's slip is the other one, moving two places for a single times ten. Ask how many tens make a hundred.
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.