Order and Compare Numbers Questions and Answers

1. Comparing Numbers

Comparing numbers is a process in which we find if one number is equal, smaller or bigger than the other number. We use the following symbols to compare two numbers:

• Equal to (=)
• Greater than (>)
• Less than (<)

1.1 Comparing Whole Numbers and Decimal Numbers

While comparing whole numbers and decimal numbers, we observe the digits of each number and compare the place values starting with the highest.

For example, 8672 > 5634,  8.672 < 56.34, 3.567 < 3.664

1.2 Comparing Fractions

We observe the denominators of the given fractions when comparing fractions. If the denominators are equal, compare the numerators.

If the denominators are unequal, find the LCM of both the denominators, and convert the fractions to equivalent fractions with LCM as the denominator.

The LCM of 7 and 5 is 35. Rewrite both the fractions as equivalent fractions with 30 as the denominator.

1.3 Comparing Negative and Positive Numbers

We consider all the following cases while comparing negative and positive numbers:

Case 1: To compare positive numbers observe the place values.

Case 2: To compare a positive number and a negative number, remember that positive numbers are always greater than negative numbers.

For example, 51.8   >  - 126

Case 3: To compare negative numbers, ignore the signs and compare the place values. Then, follow the rule ‘Bigger positive numbers are the smaller negative numbers’ and obtain the final result.

For example,  - 46 <  -19

2. Ordering Numbers

We can order numbers according to their size from smallest to largest i.e ascending order or from largest to smallest i.e.descending order. The rules for ordering the numbers are the same as comparing numbers.

2.1 Ordering Decimals

To order decimals, we need to look at each number and compare starting with the first digit.

For example, place these numbers in order, starting with the smallest:

4023, 4.023, 0.4023, 402.3, 40.03

Solution:

We observe the digits of each number and compare the place values.

0.4023 < 4.023 < 40.03 < 402.3 < 4023

Hence the correct order is 0.4023, 4.023, 40.03, 402.3, 4023.

2.2 Ordering Fractions

While ordering fractions, ensure that each fraction has the same denominator.

For example, arrange the following fractions starting with the smallest:

Solution:

Since these are unlike fractions, we find the LCM of the denominators.

LCM of 2, 8, 16 and 4 is 16.

We rewrite each fraction as equivalent fractions with 16 as the denominator.

Use the numerator to arrange the fractions in ascending order.

The final answer as per the fractions in the question:

2.3 Ordering Fractions, Decimals and Percentages

We need to convert all the fractions, decimals and percentages in the same format which helps to easily compare and order them.

For example, arrange the following numbers in ascending order:

Solution:
We convert all of these numbers in the same format - decimals.

Fractions to decimals:

Rewrite the conversions in ascending order: 0.306, 0.375, 0.41, 0.6

The final answer as per the original values in the question:

2.4 Ordering Negative and Positive Numbers

While ordering negative and positive numbers, we must remember the fact that for negative numbers, the bigger the number after the minus sign, the smaller the value of the negative number.

For example, arrange the following numbers in descending order:

5.8,  – 5.8,  – 8.5,  8.5

Solution:
Observe the digits of each number and compare the place values.

8.5  >  5.8  >  – 5.8  >  – 8.5

(Recall positives are bigger than negatives and higher positives become smaller negatives)

Hence the correct order is  8.5,  5.8,  – 5.8,  – 8.5