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.
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 a decimal in expanded form.
- Step 1
She reads the tenths place: 4, so 0.4.
Step 5: Your Turn
Practice makes it stick.
The Places
Problem 1 of 2
In 0.582, what digit is in the thousandths place?
The Count
Problem 2 of 2
How many thousandths make one hundredth?
Read the Places
1 of 4
In 0.739, what digit is in the hundredths place?
2 of 4
How many thousandths make one tenth?
3 of 4
How many thousandths make one whole?
4 of 4
In 0.061, what digit is in the tenths place?
Land on It
Build it, then check.
Put the marker on 1.
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?
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.
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.