Lesson 20 fractions as tenths and hundredths answer key

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

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.

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.

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.

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.

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

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