A tenths bar is one whole cut into 10 equal strips; a hundred grid cuts it into 100 small squares. Seven strips shaded is 0.7 or 7/10; 36 squares shaded is 0.36 or 36/100. Writing both forms side by side is how children connect decimals to the fractions they already know.
Tenths and hundredths worksheets: what is in the set
There are 7 tenths and hundredths worksheets on this page, and every one has an answer key except for any cut-out games. The first two sets use bars and grids to read decimals, the next ones ask children to shade a decimal, and the last two put tenths and hundredths on a number line.
Worksheet
What children do
Standard
Tenths Bars
Write the colored part of each bar as a decimal and a fraction.
4.NF.C.6
Hundredths Grids
Write the colored part of each grid as a decimal and a fraction.
4.NF.C.6
Shade the Decimal
Color the bars and grids to show each decimal.
4.NF.C.6
Tenths on a Grid (Set B)
Write the decimal for more shaded grids.
4.NF.C.6
Hundredths on a Grid (Set B)
More hundred grids to read.
4.NF.C.6
Tenths on a Number Line
Name the decimal at each dot from 0 to 2.
4.NF.C.6
Hundredths on a Number Line
Zoom in between two tenths.
4.NF.C.6
Tenths and hundredths: every tenth as a fraction and a percent
When children are learning tenths and hundredths, they should see each decimal as a fraction, a picture and a number. The tenths are the first decimals, and the table lists them with their fractions in simplest form and their percents. The Common Core standards for grade 4 ask children to use decimal notation for fractions with denominators 10 and 100 (4.NF.C.6). The Common Core standards for grade 4 number and operations in fractions describe them, and Wikipedia’s article on the decimal system explains the notation.
Decimal
Fraction
Simplest form
Percent
Strips shaded on a tenths bar
0.1
1/10
1/10
10%
1 of 10
0.2
2/10
1/5
20%
2 of 10
0.3
3/10
3/10
30%
3 of 10
0.4
4/10
2/5
40%
4 of 10
0.5
5/10
1/2
50%
5 of 10
0.6
6/10
3/5
60%
6 of 10
0.7
7/10
7/10
70%
7 of 10
0.8
8/10
4/5
80%
8 of 10
0.9
9/10
9/10
90%
9 of 10
Notice that 0.5 is the same as 1/2, 0.25 is 1/4 and 0.75 is 3/4. These are the decimals that children meet most often in real life, so they are worth memorizing. A tenths bar shows the first set, and the hundredths grid shows the second.
Hundredths grid: how many squares for each decimal?
A hundredths grid is a square cut into 10 columns of 10 squares. Each column is one tenth, and each square is one hundredth. To show a decimal such as 0.36, shade 3 full columns and 6 more squares. This table shows eight decimals, with the number of squares and the fraction:
Decimal
Squares shaded on a 100 grid
Full columns and extra squares
Fraction
Simplest form
0.01
1
0 columns and 1 square
1/100
1/100
0.05
5
0 columns and 5 squares
5/100
1/20
0.10
10
1 column and 0 squares
10/100
1/10
0.25
25
2 columns and 5 squares
25/100
1/4
0.36
36
3 columns and 6 squares
36/100
9/25
0.50
50
5 columns and 0 squares
50/100
1/2
0.75
75
7 columns and 5 squares
75/100
3/4
0.99
99
9 columns and 9 squares
99/100
99/100
Decimal grids worksheets: why 0.7 and 0.70 are equal
One of the most important ideas in decimal grids worksheets is that a tenth is the same as ten hundredths. Seven columns of a hundred grid are 70 squares, so 0.7 = 0.70. Many children think that 0.70 is bigger because it has more digits, and the grids show that this is not so. The table shows six tenths and the same amounts in hundredths:
Tenths
Same amount in hundredths
Columns on a hundred grid
Squares on a hundred grid
0.1
0.10
1
10
0.2
0.20
2
20
0.3
0.30
3
30
0.5
0.50
5
50
0.7
0.70
7
70
0.9
0.90
9
90
Decimals on a number line: how many numbers are in between?
A number line helps children to see decimals as numbers with a place. Between 0 and 1 there are 9 tenths and 99 hundredths, and between any two tenths there are 9 hundredths. The number line worksheet on this page zooms in between two tenths, as in the diagram above. The counts are:
none with hundredths, but 0.991 to 0.999 with thousandths
9
This idea of zooming in is how children see that there is always another number between two numbers, which is a first step towards the idea that the number line is dense. You can print a number line from the number line tool and mark the tenths and hundredths yourself.
Decimal fractions worksheets: from decimals to mixed numbers
Decimal fractions worksheets connect the two ways of writing a number less than 10. A decimal with one place is a fraction with a denominator of 10, and a decimal with two places is a fraction with a denominator of 100. When the whole part is not zero, the number is a mixed number. This table shows six decimals in three forms:
Tenths bars. Strips of one tenth.
Decimal
Mixed number
Fraction of a whole
In words
2.34
2 34/100
234/100
two and thirty-four hundredths
5.07
5 7/100
507/100
five and seven hundredths
0.60
0 60/100
60/100
sixty hundredths
3.5
3 5/10
35/10
three and five tenths
12.08
12 8/100
1208/100
twelve and eight hundredths
7.25
7 25/100
725/100
seven and twenty-five hundredths
For more about fractions with these denominators, see the fractions worksheets section, and for the place value of each digit see the page on decimal place value.
Tenths and hundredths in real life: money and measurement
Tenths and hundredths are everywhere in daily life. Money has two decimal places because there are 100 cents in a dollar, and the metric system is built on tenths and hundredths too. This table shows six examples:
Real-life measure
As a decimal
As a fraction
Why it is hundredths or tenths
A penny
$0.01
1/100 of a dollar
there are 100 cents in a dollar
A nickel
$0.05
5/100 = 1/20 of a dollar
5 cents
A dime
$0.10
1/10 of a dollar
10 cents is one tenth
A quarter
$0.25
25/100 = 1/4 of a dollar
25 cents
1 centimeter
0.01 meter
1/100 of a meter
there are 100 cm in 1 m
1 millimeter
0.1 centimeter
1/10 of a centimeter
there are 10 mm in 1 cm
The money worksheets section has more practice with decimals in money problems.
Common mistakes with tenths and hundredths
These are the mistakes that teachers see most often, with the reason and the fix:
What the child does
Why
The fix
Reads 0.05 as five tenths
The 5 is in the hundredths place
0.05 is 5 hundredths, and 0.5 is 5 tenths
Writes 3/10 as 0.03
Puts the 3 in the hundredths place
tenths have one decimal place: 0.3
Shades 4 squares for 0.4
Confuses a tenths bar with a hundredths grid
0.4 is 4 columns or 40 squares
Says 0.7 is less than 0.70
Thinks that more digits means more
they are equal: 7 columns is the same as 70 squares
Reads 0.36 as “thirty-six”
Leaves out the place name
it is thirty-six hundredths
Tenths and hundredths word problems
Word problems show where tenths and hundredths are used. Ask children to draw a bar or a grid, and then to write the decimal and the fraction:
Word problem
Working
Answer
A ribbon is cut into 10 equal parts and 3 parts are used. What decimal is used?
3/10 = 0.3
0.3
A grid has 100 squares and 45 are shaded. What decimal is shaded?
45/100 = 0.45
0.45
A pie is cut into 10 slices and 7 are eaten. What decimal is eaten?
7/10
0.7
Mia has 25 cents. What part of a dollar is that, as a decimal?
25/100
$0.25
A race is 0.6 of a kilometer. How many tenths is that?
0.6 = 6/10
6 tenths
A board is 0.08 meters thick. Write it as a fraction.
8/100
8/100 = 2/25
Games and activities for tenths and hundredths
Children learn tenths and hundredths best when they play with it. These games use things that are found at home or in a classroom:
Grid shading race: one player says a decimal and the other shades it on a hundredths grid
Decimal bingo: make a card of tenths and hundredths, and call out fractions
Coin sort: put coins in order and write the value of each as a decimal
Zoom in: start on a number line from 0 to 1, and zoom in on a tenth to find the hundredths
Match the forms: cut out cards with a decimal, a fraction, a picture and a word, and match the four
Meter stick: measure an object in centimeters and write the length as a decimal of a meter
A 20-minute lesson on tenths and hundredths
A short lesson is the best way to introduce tenths and hundredths. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:
Minutes
Activity
What to say or ask
0 to 3
Show a tenths bar and shade 3 strips
How many tenths are shaded? Write it as a fraction and a decimal.
3 to 8
Show a hundred grid and shade 0.37
How many full columns? How many squares are left?
8 to 13
Compare 0.7 and 0.70 on grids
Which is bigger? Why do they have the same amount shaded?
13 to 18
Place 0.35 on a number line between 0.3 and 0.4
Where do you zoom in?
18 to 20
Start a worksheet and check one answer
Did you write the fraction too?
Where tenths and hundredths fits across the grades
No skill stands alone. This table shows what children learn before and after tenths and hundredths, with the standard that goes with each step:
Grade
What children do
Standard or page
Grade 3
Understand fractions as parts of a whole, with denominators up to 8
This page covers the first step in grade 4. The next step is the page on decimal place value, where children name each place.
Helping at home with tenths and hundredths
Parents do not need to be experts to help with tenths and hundredths. These suggestions work well, and each takes only a few minutes:
Number line. Zoom in on 0.3 to 0.4.
Look at a price tag and ask what part of a dollar the cents are.
Measure something in centimeters and write the length in meters, such as 35 cm = 0.35 m.
Cut a chocolate bar or a sheet of paper into 10 strips and name the parts.
Ask the child to explain why 0.5 is the same as 1/2.
Use the answer keys, and let the child find and fix their own mistakes.
How to check progress in tenths and hundredths
A teacher or parent can check progress with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:
What you see
What it means
What to do next
The child reads tenths bars but not grids
The child understands tenths and needs the idea of hundredths
Cut a tenth of a bar into 10 and show that each piece is a hundredth
How to read a tenths bar or a hundredths grid, step by step
Count the equal parts in the whole. A tenths bar has 10 strips, and a hundredths grid has 100 squares. This is the denominator.
Count the shaded parts. This is the numerator, such as 4 strips or 37 squares.
Write the fraction. For example 4/10 or 37/100.
Write the decimal. A fraction with 10 in the denominator has one decimal place, and one with 100 has two: 0.4 and 0.37.
Check with the other form. Say the decimal in words (“thirty-seven hundredths”) and compare it with the fraction.
This routine works for every worksheet in the set, and it is the habit that makes tenths and hundredths easy to learn. Children who skip step 1 often count the wrong number of parts, and they make the mistakes described above.
The order in which to teach tenths and hundredths
Teachers usually follow three stages. First comes the concrete stage, where children cut real things into 10 or 100 equal parts. Next comes the pictorial stage, with the bars, grids and number lines on the worksheets. Last comes the abstract stage, where children work with the numbers alone. A child who goes straight to the abstract stage often learns the rules without understanding them, so it is worth spending time with the pictures, even when the child seems ready for the numbers.
A five-day plan for tenths and hundredths
Most children need about a week of short sessions for tenths and hundredths. This plan follows the order of the worksheets on this page:
Day
What to do
Practice
Day 1
Tenths bars: shade and name the decimal and the fraction
Yes. On a hundred grid, 7 tenths covers the same area as 70 hundredths.
How do you write 36 hundredths as a decimal?
0.36: the 3 is in the tenths place and the 6 is in the hundredths place.
What is the difference between tenths and hundredths?
A tenth is one part of a whole cut into 10 equal parts, and a hundredth is one part of a whole cut into 100 equal parts. One tenth equals ten hundredths, so 0.1 = 0.10.
How do you read 0.36?
Read it as “thirty-six hundredths”. Reading it as “zero point three six” is also correct, but “thirty-six hundredths” shows that the child understands the place value.
When do children learn tenths and hundredths?
Children learn them in grade 4 (4.NF.C.5 to 4.NF.C.7) after they have learned fractions in grade 3. Many classes start them in the second half of grade 3.
