Tenths and Hundredths

In Mathematics, tenths and hundredths are defined for the place value of digits that comes after a decimal point. Ones, tens, hundreds, thousands are the place value of the digits in a number when we move from right to left. But, if a number is a decimal number, then what are the place values of digits that come after the decimal point? Thus, tenths and hundredths are the place values of the digits after decimal places. For example, for 3.45, the tenth place has digit 4 and the hundredth place has digit 5.

  • Tenths → 1/10th
  • Hundredths → 1/100th

Learn more about tenths and hundredths in this article with solved problems. Students of Class 4, 5 and 6 can make use of this article to learn the place value of numbers in decimals.

What is Tenths?

Tenths is the place value of the digit that appears after the decimal. It represents the 1/10 position of the digit. For example,

1cm = 10 mm

But, 1 mm = 1/10 cm = 0.1 cm

Therefore, 1 mm is equal to one-tenth cm.

Place Value Table for Tenths

Hundreds

Tens

Ones

Tenths

(100)

(10)

(1)

(1/10)

The above place value table shows the way of representation of a decimal number that has digits at the place of hundreds, tens, ones and tenths.

Note:

  • Tens and Tenths, both are different place values
  • Hundreds and Hundredths, both are different place values

Fractions as Decimals

A fraction has two parts, numerator and denominator. Thus, if the denominator of a fraction is 10, then we can represent it as a decimal number with a digit present in the tenths place.

For example, if the fraction is 11/5, then it can be written as:

(11/5) x (2/2) = 22/10 = 20/10 + 2/10 = 2 + 2/10 = 2 + 0.2 = 2.2

Let us see some more examples of expressing the decimals with the place value table as we have discussed above.

Decimals Related Articles

Solved Examples on Tenths

Example 1: Write the following numbers in the place value table :

(a) 10.5

(b) 4.8

(c) 111.1

(d) 10.10

Solution: Let us create a single place value chart for all the numbers.

Numbers

Hundreds (100)

Tens (10)

Ones (1)

Tenths (1/10)

10.5

0

1

0

5

4.8

0

0

4

8

111.1

1

1

1

1

10.10

0

1

0

1

Example 2: Write the following as decimals.

(a) Three ones and one-tenths

(b) Forty and five-tenth

Solution: (a) Three ones and one-tenths

Three ones means 3 comes in ones place and one-tenths means 1/10

Therefore,

Three ones and one-tenths = 3 + 1/10 = 3 + 0.1 = 3.1

(b) Forty and five-tenth

Forty → 40

Five-tenth → 5/10 = 0.5

Therefore,

Forty and five-tenth = 40 + 0.5 = 40.5

Example 3: Write the following as decimals.

(a) 6/10

(b) 100 + 50 + 2 + 2/10

(c) 99/10

(d) ⅖

Solution:

(a) 6/10 = 0.6

(b) 100 + 50 + 2 + 2/10 = 100 + 50 + 2 + 0.2

= 152 + 0.2

= 152.2

(c) 99/100 = (99/10) x (1/10) = 9.9 x (1/10) = 9.9/10 = 0.99

(d) ⅖ = (2×2)/(5×2) = 4/10 = 0.4

Example 4: Write the decimals into fractions and reduce them into the lowest form.

(a) 0.7

(b) 3.5

(c) 2.0

(d) 3.9

Solution:

(a) 0.7

Multiplying and dividing by 10, we get;

= 0.7 x (10/10)

= 7/10

(b) 3.5

Multiplying and dividing by 10, we get;

= 3.5 x (10/10)

= 35/10

Since 5 x 7 = 35 and 5 x 2 = 10, therefore, reducing the above fraction in lowest form, we get;

= 7/2

(c) 2.0

2.0 = 20/10 = 2

(d) 3.9

Multiplying and dividing by 10, we get;

= 3.9 x (10/10)

= 39/10

Example 5: Write the following as cm using decimals.

(a) 5 mm

(b) 40 mm

(c) 120 mm

Solution: As we know,

1 cm = 10 mm

Therefore,

1 mm = 1/10 cm = 0.1 cm

(a) 5 mm

5mm = 5/10 cm = 0.5 cm

(b) 40 mm

40 mm = 40/10 cm = 4cm = 4.0 cm

(c) 120 mm

120 mm = 120/10 cm = 12 cm = 12.0 cm

What is Hundredths?

Hundredths after decimal points shows 1/100th part of a whole. It represents the place value of the digit that occurs two places after the decimal. For example, for 3.45, 5 is at hundredth place.

As we know,

1 meter = 100 cm

So, 1 cm = 1/100 m = 0.01 m

Thus, we can say, 1 cm is the (1/100)th of a meter.

Ones

Tenths

Hundredths

(1)

(1/10)

(1/100)

Solved Examples on Hundredths

Example 1: Write the following numbers in the place value table :

(a) 10.53

(b) 4.81

(c) 111.15

(d) 10.18

Solution: Let us create a single place value chart for all the numbers.

Numbers

Hundreds (100)

Tens (10)

Ones (1)

Tenths (1/10)

Hundreths (1/100)

10.53

0

1

0

5

3

4.81

0

0

4

8

1

111.15

1

1

1

1

5

10.18

0

1

0

1

8

Example 2: The place value of the digits are given in the below table. Write the numbers.

Hundreds (100)

Tens (10)

Ones (1)

Tenths (1/10)

Hundreths (1/100)

(a)

2

1

1

3

2

(b)

0

8

0

8

1

(c)

1

2

3

4

5

(d)

0

0

9

0

8

Solution:

(a) The number is:

⇒ 2 x 100 + 1 x 10 + 1 x 1 + 3 x 1/10 + 2 x 1/100

⇒ 200 + 10 + 1 + 0.3 + 0.02

⇒ 211+0.32

⇒ 211.32

(b) The number is:

⇒ 0 x 100 + 8 x 10 + 0 x 0 + 8 x 1/10 + 1 x 1/100

⇒ 0 + 80 + 0 + 0.8 + 0.01

⇒ 80 + 0.81

⇒ 80.81

(c) The number is:

⇒ 1 x 100 + 2 x 10 + 3 x 1 + 4 x 1/10 + 5 x 1/100

⇒ 100 + 20 + 3 + 0.4 + 0.05

⇒ 123 + 0.45

⇒ 123.45

(d) The number is:

⇒ 0 x 100 + 0 x 10 + 1 x 9 + 0 x 1/10 + 8 x 1/100

⇒ 0 + 0 + 9 + 0 + 0.08

⇒ 9 + 0.08

⇒ 9.08

Example 3: Write the following as decimals.

(a) Three ones and one-hundredth

(b) Forty and five-hundredth

Solution:

(a) Three ones and one-hundredth

Three ones = 3 x 1 = 3

One-hundredth = 1/100 = 0.01

Therefore, the required decimal is:

3 x 1 + 1/100 = 3 + 0.01 = 3.01

(b) Four hundred six and five-hundredth

Solution:

Four hundred six – 406

Five-hundredth – 5/100

Therefore, the required decimal is:

406 + 5/100

= 406 + 0.05

= 406.05

Practice Questions on Tenths and Hundredths

Q.1: Write the following numbers in the place value table:

  • 34.5
  • 4.9
  • 9.87
  • 11.01

Q.2: Write the following as decimals.

  • Two hundred two and three tenths
  • One and nine hundredths
  • Eighty and five tenths
  • Four and sixty five hundredths

Q.3: Write the decimals into fraction form.

  • 2.25
  • 0.8
  • 4.5
  • 1.25

Q.4: Write the following into decimal form.

  • 40 + 1/10 + 3/100
  • 12 + 9/10 + 1/1000

Frequently Asked Questions on Tenths and Hundredths

Q1

What are tenths and hundredths?

Tenth is the place value that represents the position of digit after decimal place equal to 1/10th and hundredth represents the position of digit in a number after decimal place equal to 1/100th. For example, nine tenths is equal to 9/10 = 0.9 and 5 hundredth is equal to 5/100 = 0.05.

Q2

How to write 10 paise in rupees?

As we know, 1 rupee = 100 paise
1 paise = 1/100 rupees = 0.01 rupees
So, 10 paise = 10 x 0.01 rupees = 0.1 rupees

Q3

What are the examples of tenths?

The examples of tenths are:
Tenths of 98 = 98/10 = 9.8
Tenths of 23 = 23/10 = 2.3

Q4

What are the examples of hundredths?

The examples of hundredths are:
612/100 = 6.12, where 2 is at hundredth place
921/100 = 9.21, where 1 is at hundredth place

Q5

What is one and seventy two hundredths?

One and seventy two hundredths is 1.72.

Q6

What is the lowest fraction form of 0.04?

0.04 = 4/100 = 1/25. Therefore, the lowest fraction form of 0.04 is 1/25.

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