Cut each hundredth into ten again. That gives thousandths, the third place after the point.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Try it first
In 0.46, the 4 is worth 4 tenths. What is the 6 worth?
Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.
Reading it aloud
0.325 is read "three hundred twenty-five thousandths". The last place names the whole thing.
Expanded form
0.325 is 0.3 + 0.02 + 0.005, or 3/10 + 2/100 + 5/1000.
Where "and" goes
In 4.6 the word "and" marks the point: "four and six tenths".
Step 2: Try It Yourself
Tap and try it out.
0.325 = 3/10 + 2/100 + 5/1000 = 325/1000, read as three hundred twenty-five thousandths.
The dot never moves. Each line is a closer look at the one above it, and each look reads one more digit.
Step 3: In Real Life
A race timer
A sprint timer reads 9.582 seconds. The 2 is two thousandths of a second. Races are won and lost in the third place after the point.
Step 4: Watch an Example
One step at a time.
Watch Ana Write 0.407
Ana writes 0.407 in expanded form.
- Step 1
The 4 sits in the tenths place, so it is worth 0.4.
Watch Leo Write Sixty-Four Thousandths
Leo hears "sixty-four thousandths" and writes it down. He starts, and you finish.
- Step 1
The name of a decimal comes from its smallest place.
Step 5: Your Turn
Practice makes it stick.
The Paper Strip
Problem 1 of 12
A strip is cut into ten equal pieces. One piece is cut into ten again. Then one of those is cut into ten again. How big is the smallest piece?
The Race Clock
Problem 2 of 12
A clock reads nine and six thousandths of a second. How is that written?
Read the Places
Name the place first. Then answer.
Problem 3 of 12
In 0.836, which digit is in the hundredths place?
Problem 4 of 12
Write 0.5 + 0.03 + 0.008 as one decimal.
Problem 5 of 12
80 thousandths is the same as how many hundredths?
Find the Mistake
One line on each page is a slip. Find it, then fix it.
Problem 6 of 12
Priya writes 0.802 in expanded form. One line is a slip. Which?
Priya's page for 0.802
- 10.802
- 28 tenths and 2 hundredths
- Answer0.802 = 0.8 + 0.02
Problem 7 of 12
What is 0.802 in expanded form?
Problem 8 of 12
Sam writes four thousandths as a decimal. One line is a slip. Which?
Sam's page for four thousandths
- 1four thousandths
- 2thousandths is the second place after the point
- Answerfour thousandths = 0.04
Problem 9 of 12
What is four thousandths as a decimal?
Which Way?
Pick the way that starts right.
Problem 10 of 12
Ana wants to read 0.063 out loud. Which way?
Problem 11 of 12
Dev wants to know how many thousandths are in one whole. Which way?
Build the Number
Build it, then check.
Problem 12 of 12
Build a number with no tenths, 4 hundredths and 9 thousandths.
0.000 = 0/10 + 0/100 + 0/1000 = 0/1000, read as zero thousandths.
The dot never moves. Each line is a closer look at the one above it, and each look reads one more digit.
Step 6: Quick Check
Show what you know.
Question 1 of 2
In 0.914, what digit is in the thousandths place?
Question 2 of 2
How many thousandths make one hundredth?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 2
Maya writes the digits 3, 0 and 3 after the point. The two 3s are as far apart as they can be. What is the number?
Stretch 2 of 2
A number is read "four hundred twenty thousandths". Which place holds its 2?
What You Learned
- Thousandths are the third place after the point.
- Read a decimal by naming its last place.
- Expanded form splits it place by place.
For the grown-up
This lesson is where the child reads and writes decimals to thousandths in numerals, words, and expanded form. 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 writing the digits straight after the point without counting places: four thousandths as 0.4, sixty-four thousandths as 0.64. The cure is to count the three places out loud — tenths, hundredths, thousandths — and fill the empty ones with zeros before writing the digits. Priya’s slip is the same error read backwards, taking the third digit of 0.802 to be hundredths.
One more cut — Split each hundredth into ten and you have thousandths. Three decimal places means thousandths: 0.472 is 4 tenths, 7 hundredths and 2 thousandths — or 472 thousandths altogether. Both readings describe the same number and each is useful in different situations.
Reading them correctly — 0.472 is "four hundred seventy-two thousandths". The place name comes from the last digit, since that is the smallest unit present. Saying it in full keeps the fractional meaning alive and makes comparisons much easier to reason about.
Where thousandths appear — A millimeter is a thousandth of a meter. Engineering tolerances, medicine doses and athletics times all use three decimal places routinely — an Olympic sprint can be decided by 0.003 of a second. The precision is not academic.
The fraction underneath — 0.472 is 472/1000. Every terminating decimal is a fraction whose denominator is a power of ten, which is exactly why decimals and fractions can always be converted between. Seeing the fraction makes the size of a small decimal much easier to judge.
One more cut — A hundredth cut into ten gives a thousandth: 0.001 0.456 is 4 tenths, 5 hundredths, 6 thousandths. As a fraction: 456/1000 Say it out loud as "four hundred and fifty-six thousandths" and the fraction is obvious.