Decimals · Grades 4, 5

Decimal Place Value: Reading and Writing Decimals

Quick answer

Each place after the decimal point is worth a tenth of the one before it: tenths, then hundredths, then thousandths. The decimal point marks where the whole numbers end. Read 3.47 as "three and forty-seven hundredths", because the last digit sits in the hundredths place and names the whole decimal part.

What you'll learn

  • Name the value of each place after the decimal point
  • Read and write a decimal in words and in expanded form
  • Explain why trailing zeros do not change a decimal's value

Every place is a tenth of the one before

Place value did not change when the decimal point arrived. Moving left, each place is worth ten times the one before; moving right, each is worth a tenth.

PlaceValueIn 3.4723.472
ones1133
tenths110=0.1\tfrac{1}{10} = 0.144
hundredths1100=0.01\tfrac{1}{100} = 0.0177
thousandths11000=0.001\tfrac{1}{1000} = 0.00122

The decimal point is not a place of its own. It is a marker showing where the whole numbers stop.

Why the names end in -ths

A tenth is one part of a whole cut into ten. That is a fraction, and the place names are its denominators read aloud.

0.4=4100.07=71000.002=210000.4 = \frac{4}{10} \qquad 0.07 = \frac{7}{100} \qquad 0.002 = \frac{2}{1000}

So decimals are not a separate number system. They are fractions whose denominators are always 1010, 100100, 10001000 and so on — which is exactly why they line up in columns and ordinary fractions do not.

Reading one aloud

  1. Read the whole-number part.
  2. Say “and” for the point.
  3. Read the decimal digits as a whole number.
  4. Say the name of the last place.
3.47⟶"three and forty-seven hundredths"3.47 \quad\longrightarrow\quad \text{"three and forty-seven hundredths"}

The last digit is in the hundredths place, so the whole decimal part is counted in hundredths — forty-seven of them.

DecimalSaid aloud
0.60.6six tenths
0.250.25twenty-five hundredths
5.085.08five and eight hundredths
1.2041.204one and two hundred four thousandths

Saying “three point four seven” is fine in conversation, but the “-ths” version is the one that tells you what the number is worth.

Expanded form

Writing every place out separately shows where the value lives.

3.47=3+0.4+0.073.47 = 3 + 0.4 + 0.07 3.47=(3×1)+(4×110)+(7×1100)3.47 = (3 \times 1) + \left(4 \times \tfrac{1}{10}\right) + \left(7 \times \tfrac{1}{100}\right)

The 44 and the 77 are not “four and seven”. They are four tenths and seven hundredths, and the 44 is worth far more than the 77 despite being the smaller digit.

Zeros that matter and zeros that do not

0.5=0.50=0.5000.5 = 0.50 = 0.500

A zero on the end adds nothing. Five tenths and fifty hundredths are the same amount — cutting each tenth into ten pieces gives ten times as many pieces of a tenth the size.

0.5=510=50100=0.500.5 = \frac{5}{10} = \frac{50}{100} = 0.50

That is equivalent fractions, in decimal clothing.

A zero between the point and the digits is doing real work:

0.5≠0.050.5 \ne 0.05

The second is ten times smaller, because the zero pushed the 55 out of the tenths place and into the hundredths.

Worked examples

Common mistakes

Practice problems

  1. In 5.3725.372, which place is the 77 in?

    Answer

    Hundredths.

    Full solution

    Counting right from the point: 33 is tenths, 77 is hundredths, 22 is thousandths.

  2. What is the 99 worth in 2.092.09?

    Answer

    Nine hundredths, or 0.090.09.

    Full solution

    The zero holds the tenths place, so the 99 sits in hundredths: 9100\tfrac{9}{100}.

  3. Write 0.80.8 in words.

    Answer

    Eight tenths.

    Full solution

    One digit after the point means tenths, and there are eight of them.

  4. Write 12.4512.45 in words.

    Answer

    Twelve and forty-five hundredths.

    Full solution

    The last digit is in the hundredths place, so the decimal part is forty-five hundredths.

  5. Write “three and seven hundredths” as a decimal.

    Hint

    Hundredths needs two places after the point.

    Answer

    3.073.07

    Full solution

    Seven hundredths fills two places as 0707, so the answer is 3.073.07.

    Writing 3.73.7 would say seven tenths, ten times as much.

  6. Write 6.046.04 in expanded form.

    Answer

    6+0.046 + 0.04

    Full solution

    The tenths place is empty, so only the ones and hundredths contribute.

  7. Write 0.60.6 as a fraction in simplest form.

    Answer

    35\tfrac{3}{5}

    Full solution

    One decimal place means tenths: 610\tfrac{6}{10}, which simplifies to 35\tfrac{3}{5}.

  8. Are 0.70.7 and 0.700.70 the same number?

    Answer

    Yes.

    Full solution

    710=70100\tfrac{7}{10} = \tfrac{70}{100}, so the two are equal. A zero on the end changes how the number is written, not what it is worth.

  9. Which is bigger, 0.30.3 or 0.280.28?

    Hint

    Compare the tenths place first.

    Answer

    0.30.3

    Full solution

    0.30.3 has three tenths; 0.280.28 has only two. Three tenths beats two tenths whatever follows.

    Writing 0.30.3 as 0.300.30 makes it plain: 3030 hundredths against 2828.

  10. Ana says 0.450.45 is bigger than 0.50.5 because 4545 is bigger than 55. Explain what she has missed.

    Hint

    What is each digit actually worth?

    Answer

    She compared the digits as whole numbers. 0.50.5 is bigger.

    Full solution

    In 0.450.45 the 44 is four tenths. In 0.50.5 the 55 is five tenths. Five tenths beats four tenths, so 0.50.5 is the larger number.

    Writing both with two places settles it: 0.450.45 against 0.500.50.

    Digits after the point are worth less the further right they sit, so a longer decimal is not automatically a bigger one.

Frequently asked questions

What are the places after the decimal point called?

Tenths, hundredths, thousandths, then ten-thousandths. Each one is a tenth of the place before it, and each name ends in -ths because it is a part of one whole.

How do I read 3.47 out loud?

Three and forty-seven hundredths. Read the whole-number part, say and for the point, then read the decimal digits as a whole number followed by the name of the last place.

Does 0.5 equal 0.50?

Yes. Five tenths and fifty hundredths are the same amount, because adding a zero at the end multiplies both the top and the bottom of the hidden fraction by ten. Zeros in front of the digits are different and do change the value.

Why is there no oneths place?

Because that place already exists — it is the ones place, on the left of the point. The places to the right start at tenths, since a tenth is the first thing smaller than one.

What does the decimal point actually do?

It marks where the whole numbers stop. The digits on its left count whole units and the digits on its right count parts of one, and the point is the boundary between them.

What to learn next

Key terms in this lesson

Decimal
A decimal writes a number using places smaller than one, separated from the whole part by a decimal point. 3.47 is three wholes plus four tenths plus seven hundredths.
Place value
Place value is the idea that a digit's worth depends on where it sits. The 4 in 40 is worth forty; the 4 in 0.4 is worth four tenths.

Standards alignment

This lesson covers the following Common Core State Standards for Mathematics.

  • CCSS.MATH.CONTENT.5.NBT.A.1Number and Operations in Base TenRecognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
  • CCSS.MATH.CONTENT.5.NBT.A.3Number and Operations in Base TenRead, write, and compare decimals to thousandths.
  • CCSS.MATH.CONTENT.5.NBT.A.3aNumber and Operations in Base TenRead and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
For teachersTick to print a blank worksheet; leave it clear to print the lesson with the full answer key.