﻿ Equivalent Decimals Worksheet | Problems & Solutions Equivalent Decimals Worksheet

Equivalent Decimals Worksheet
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1.
Compare 0.80 and 0.8 using models. a. 0.80 ≤ 0.8 b. 0.80 < 0.8 c. 0.80 = 0.8 d. 0.80 > 0.8

Solution:

0.80 is equivalent to 80 hundredths. It can be represented by a model in which 80 out of 100 parts are shaded as shown below.

0.8 is equivalent to 8 tenths. It can be represented by a model in which 8 out of 10 parts are shaded as shown below.

The shaded portion is equal in both the models.

0.80 = 0.8
[They are equivalent decimals.]

2.
What can be inferred from the models?  a. The numbers are not equivalent. b. The numbers are repeating numbers. c. The numbers are terminating decimals. d. The numbers are equivalent decimals.

Solution:

In the first model, each part represents one hundredth and 50 out of 100 parts are shaded.

The decimal equivalent for the first model is 0.50

In the second model, each part represents one tenth and five out of 10 parts are shaded.

The decimal equivalent for the second model is 0.5

50 hundredths is equal to 5 tenths.

It can be inferred that the numbers are equivalent decimals.

3.
Mr. John ate 0.2 part of pizza and his friend ate 0.20 part of the same pizza. Find the ratio between the parts they ate. a. 5:1 b. 1:2 c. 1:1 d. 2:1

Solution:

0.2 means 2 of 10 parts and 0.20 means 20 of 100 parts.

2 out of 10 parts is same as 20 out of 100 parts.

0.2 and 0.20 both are equivalent decimals.

They both ate the same quantity of the pizza.

So, the ratio of the quantities they ate is 1:1.

4.
The first model represents the quantity of the ice cream that Nina ate and the second model represents the quantity of the ice cream John ate. What do you infer from the models?  a. John ate more quantity of ice cream. b. Nina ate more quantity of ice cream. c. Both John and Nina ate the same amount of ice cream d. Nina ate less quantity of ice cream.

Solution:

From the models, the amount shaded is same for both the models.

So, they both ate the same amount of ice cream.

5.
Find the equivalent decimals for the shaded areas in the models.  a. 0.30 and 0.3 b. 3.0 and 0.3 c. 30 and 3 d. 0.030 and 0.30

Solution:

In the first model thirty out of 100 parts are shaded. So it is equal to thirty hundredths.

The decimal equivalent for the first model is 0.30

In the second model three out of 10 parts are shaded. So it is equal to three tenths.

The decimal equivalent for the second model is 0.3

6.
Write the decimal equivalents for the shaded areas in the models.  a. 0.90 and 0.070 b. 90 and 7 c. 0.90 and 0.7 d. 90 and 70

Solution:

In the first model 90 out of 100 parts are shaded. So it is equal to ninety hundredths.

The decimal equivalent for the first model is 0.90.

In the second model seven out of 10 parts are shaded. So it is equal to seven tenths.

The decimal equivalent for the second model is 0.7

7.
What can be inferred from the shaded areas in the models?  a. The numbers are repeating numbers b. The numbers are equivalent decimals c. The numbers are not equivalent decimals d. The numbers are terminating decimals

Solution:

In the first model thirty out of 100 parts are shaded. It is equal to thirty hundredths.

The decimal equivalent for the first model is 0.30.

In the second model 6 out of 10 parts are shaded. It is equal to six tenths.

The decimal equivalent for the second model is 0.6

In the first model, three columns are shaded where as in the second model 6 such columns are shaded. 30 parts in 100 are not equal to 6 parts in 10.

The numbers are not equivalent decimals.

8.
What can be inferred from the shaded areas in the models?  a. The numbers are repeating numbers b. The numbers are equivalent decimals c. The numbers are terminating decimals d. The numbers are not equivalent decimals

Solution:

In the first model 54 out of 100 parts are shaded. It is equal to fifty four hundredths.

The decimal equivalent for the first model is 0.54

In the second model 6 out of 10 parts are shaded. It is equal to six tenths.

The decimal equivalent for the second model is 0.6

0.54 parts in 100 are not equal to 6 parts in 10.

The numbers are not equivalent decimals.

9.
The heights of Frank's children are 3.8 ft and 3.80 ft. Are the two heights the same? a. Yes b. No

Solution:

3.8 represents 3 and 8 tenths. 3.80 represents 3 and 80 hundredths.

As 8 tenths equals 80 hundredths, 3.8 and 3.80 are equivalent decimals.

So, the two heights are same.

10.
Is 4.2 equivalent to 4.02? a. Yes b. No

Solution:

Compare the integer parts of the numbers. Both are equal to 4.

Now compare the decimal parts.

The decimal part of 4.2 is 0.2 which is equivalent to 2 tenths.

The decimal part of 4.02 is 0.02 which is equivalent to 2 hundredths.

2 tenths is greater than 2 hundredths.

So 4.2 > 4.02

They are not equivalent decimals.