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# Comparing Decimals

Comparing decimals is alike to comparing whole numbers when we compare decimals we use place value or a number line.

Mathematical Concepts in Comparing Decimals:

• To compare decimals start at the left and compare digits in the same places, find first the place where the decimals differs.
• Equal decimals can be written by adding zeros or deleting zeros from the right of the last non zero digit.
• Adding zeros at the end of the decimal does not change it value. On the other hand, adding zeros before the first decimals digit changes its value.
• To compare and order decimals having different number of digits, put zeros at the end of the shorter decimals to have the same number of digits, then  compare and order the numbers as if the decimal points.

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## Comparing and Ordering Decimals

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• Compare and order decimals through hundred thousandths.
• Use the symbols >, <, or = correctly in comparing decimals.
• List decimal in the order least to greatest.

Problem in comparing and ordering decimals:

When you compare decimals, think about place value you can add or remove zeros at the end of the decimal without changing its meaning.

0.2 = 0.20 = 0.200 = 0.2000

0.54 = 0.540 = 0.5400 = 0.54000

3.5 = 3.50 = 3.500 = 3.5000

The ordering decimal is 3.5, 0.2, 0.54.

### Solved Examples

Question 1: Which is greater 0.34 or 0.320?
Solution:
0.34 = 34 hundredths, 0.320 = 32 hundredths

34 hundredths is greater than 32 hundredths.

The comparing is 0.34 > 0.320.

Question 2: Which is greater, 5.671 or 5.67?
Solution:
5.671 = 5 and 671 thousandths, 5.670 = 5 and 670 thousandths

5.671 is greater than 5.67

The comparing and ordering decimals is 5.671 > 5.67

## How to Compare Decimals

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Suppose if we have a two decimal numbers we can compare them. Normally one number is greater than, less than or equal to another number. Here we are going to see some examples for how to compare and order decimal values.

### Solved Examples

Question 1: Compare 12.45 and 5.7.
Solution:
Step 1: First we need to compare the whole numbers.

Step 2: Here the whole numbers are 12 and 5 .

Step 3: S0 12 > 5 .

Step 4: Here 12.45 is greater than 5.7.

Question 2: Compare 0.4 and $\frac{2}{5}$
Solution:
Step 1: First we need to convert $\frac{2}{5}$ as a decimal value. So we get $\frac{2}{5}$ = 0.4

Step 2: Now we have 0.4 and 0.4.

Step 3: Here both are equal.

Step 4: So the answer is 0.4 = 0.4.

## Comparing Decimals Examples

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Below you could see comparing decimals examples

### Solved Examples

Question 1: 6.34, 6.36, 5.31, 6.51
Solution:

Compare the whole numbers first 5.33 is the least

Compare the number places next 6.51 is the greatest

6.34 and 6.36 have the same tenths place.

Compare the hundredths places 6.34 < 6.36

After comparing and ordering decimals = 6.51, 6.36, 6.34 and 5.33.

Question 2: 8.34, 8.27, 8.39, 8.23
Solution:

From compare the whole numbers: all the whole numbers are 8

Compare the digits in the tenths places 2<3.

Compare the hundredths places of 8.27 and 8.23: 3<7, so 8.23 < 8.27

Compare the hundredths places of 8.23 and 8.39; 4<9, so 8.34< 8.39

After Ordering and comparing decimal places = 8.23, 8.27, 8.34, and 8.39

## Practice Problems

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Problem 1: Aren obtained 65 out of 100 in Maths and 75 out of 150 in History. In which subject he scored better?

Problem 2: In an election 700 people out of 1200 will vote for Exxal party in constituency A and 900 out of 1900 will vote for the same party in constituency B. The party fared better in which constituency?

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