How to Compare Decimals

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A decimal is a number that consists of a whole number and a fractional part. To put it in another way, decimals are fractions and mixed numbers with denominators that are powers of 10. For example, the decimal \(0.6\) is the same as the fraction \({ 6 \over 10}\) , or the decimal \(1.2\) is the same as fraction \({12 \over 10}\) or the mixed number \(1{1 \over 5}\) . You can change Fractions and mixed numbers to decimals. For instance, instead of writing \(4 \over 5\) you can write \(0.8\) . Below are few steps for comparing two decimals:

Steps To compare two decimals:
Step 1: Compare the whole parts first. if the whole part of one decimal is greater, it means that this decimal is greater than the other.
Step 2: But if the whole parts are the same, compare the decimals from the left. (hundreds, tens, ones, tenth, hundredth, etc.)
Step 3: To compare decimals, use the following symbols:
Equal to \(=\)
Less than\( \lt\)
Greater than \(\gt\)
Greater than or equal \(\geq\)
Less than or equal \(\leq\)

Example:
\(2.67 \gt 0.267\)

Free printable Worksheets

Exercises for Comparing Decimals

1) \(43.97 \ \bbox[5px,border:2px solid black] { } \ 2.83\)

2) \(58.75 \ \bbox[5px,border:2px solid black] { } \ 55.24\)

3) \(65.5 \ \bbox[5px,border:2px solid black] { } \ 42.81\)

4) \(6.18 \ \bbox[5px,border:2px solid black] { } \ 6.18\)

5) \(199.5 \ \bbox[5px,border:2px solid black] { } \ 19.95\)

6) \(462.7 \ \bbox[5px,border:2px solid black] { } \ 46.27\)

7) \(13.24 \ \bbox[5px,border:2px solid black] { } \ 13.29\)

8) \(789.5 \ \bbox[5px,border:2px solid black] { } \ 78.95\)

9) \(31.43 \ \bbox[5px,border:2px solid black] { } \ 31.62\)

10) \(46.82 \ \bbox[5px,border:2px solid black] { } \ 15.66\)

Answers

1)\(43.97 \ \bbox[5px,border:2px solid black] {\color{red}{\gt}} \ 2.83\)

Solution:
In this example, because the whole number of \(43.97\) is greater than \(2.83\) , therefore \(43.97 \ \bbox[5px,border:2px solid black] {\color{red}{\gt}} \ 2.83\)

2) \(58.75 \ \bbox[5px,border:2px solid black] {\color{red}{\gt}} \ 55.24\)

Solution:
In this example, because the whole number of \(58.75\) is greater than \(55.24\) , therefore \(58.75 \ \bbox[5px,border:2px solid black] {\color{red}{\gt}} \ 55.24\)

3) \(65.5 \ \bbox[5px,border:2px solid black] {\color{red}{\gt}} \ 42.81\)

Solution:
In this example, because the whole number of \(65.5\) is greater than \(42.81\) , therefore \(65.5 \ \bbox[5px,border:2px solid black] {\color{red}{\gt}} \ 42.81\)

4) \(6.18 \ \bbox[5px,border:2px solid black] {\color{red}{=}} \ 6.18\)

Solution:
In this example, because the whole numbers and fractional parts are the same. Therefore they are equal: \(6.18 \ \bbox[5px,border:2px solid black] {\color{red}{=}} \ 6.18\)

5) \(199.5 \ \bbox[5px,border:2px solid black] {\color{red}{\gt}} \ 19.95\)

Solution:
In this example, because the whole number of \(199.5 \) is greater than \(19.95\) , therefore \(199.5 \ \bbox[5px,border:2px solid black] {\color{red}{\gt}} \ 19.95\)

6) \(462.7 \ \bbox[5px,border:2px solid black] {\color{red}{\gt}} \ 46.27\)

Solution:
In this example, because the whole number of \(462.7\) is greater than \(46.27\) , therefore \(462.7 \ \bbox[5px,border:2px solid black] {\color{red}{\gt}} \ 46.27\)

7) \(13.24 \ \bbox[5px,border:2px solid black] {\color{red}{\lt}} \ 13.29\)

Solution
In this example, the whole numbers are the same, therefore we compare the fractional parts. Since the fraction part \(0.29\) is greater than \(0.24\) , so \(13.24 \ \bbox[5px,border:2px solid black] {\color{red}{\lt}} \ 13.29\)

8) \(789.5 \ \bbox[5px,border:2px solid black] {\color{red}{\gt}} \ 78.95\)

Solution:
In this example, because the whole number of \(789.5\) is greater than \(78.95\) , therefore \(789.5 \ \bbox[5px,border:2px solid black] {\color{red}{\gt}} \ 78.95\)

9) \(31.43 \ \bbox[5px,border:2px solid black] {\color{red}{\lt}} \ 31.62\)

Solution
In this example, the whole numbers are the same, therefore we compare the fractional parts. Since the fraction part \(0.62\) is greater than \(0.43\) , so \(13.43 \ \bbox[5px,border:2px solid black] {\color{red}{\lt}} \ 13.62\)

10) \(46.82 \ \bbox[5px,border:2px solid black] {\color{red}{\gt}} \ 15.66\)

Solution:
In this example, because the whole number of \(46.82\) is greater than \(15.66\) , therefore \(46.82 \ \bbox[5px,border:2px solid black] {\color{red}{\gt}} \ 15.66\)

How to Compare Decimals