Comparing Decimals on a Number Line: Up to Thousandths

Comparing Decimals on a Number Line – Introduction

In mathematics, especially when dealing with numbers less than one, decimals play a crucial role. The ability to compare decimals is not only a fundamental math skill but also a practical one used in everyday life, such as in financial literacy and measurements. Doing so on the number line allows students to visualize the distances between different decimals with ease.

Understanding Decimal Numbers – Definition

Decimal numbers are a representation of numbers that include a whole number and a fractional part, separated by a decimal point.

The fraction part can extend to tenths, hundredths, thousandths, and beyond. For instance, in the decimal number 0.256, '0' is the whole number part, and '256' is the fractional part indicating 256 thousandths.

Decimals help us to write numbers that are not whole and represent fractions in a way that is easy to understand and use, especially when dealing with measurement, money, or data that requires precision.

Comparing Decimals on a Number Line – Example

Steps to Compare Decimals

1. Start by comparing the whole number parts. If they are different, the number with the larger whole number is greater.
2. If the whole numbers are the same, compare the next digit to the right (tenths, hundredths, etc.).
3. Place the decimals on a number line if visual comparison aids understanding.
Which is greater: 0.58 or 0.6?

Comparing Decimals on a Number Line – Guided Practice

Using our number line:

1. Notice that the whole numbers are the same, so we look at the tenth’s place. They are both 4, so we move to the next digit.
2. In the hundredths place, one number has a 5 and one has a 6. Since 6 is greater than 5, 0.465 is greater than 0.458.

Comparing Decimals on a Number Line – Practice

Practicing comparing decimals on a number line.

You're at a store and see two different weights for apples: 1.356 kg and 1.35 kg. Which bag has more apples?

Comparing Decimals on a Number Line – Summary

Key Learnings from this Text:

• Decimals represent numbers that include both a whole number and a fractional part.
• Comparing decimals involves looking at the digits from left to right and using place value.
• A number line is an effective visual tool for comparing the size of decimal numbers.
• Decimals are extensively used in real-life contexts such as money and measurements.

Explore other content on our website platform for interactive practice problems, videos, and printable worksheets to further your understanding of decimals and other math concepts.

Comparing Decimals on a Number Line – Frequently Asked Questions

Why is it important to compare decimals?
What does the decimal point represent?
How do you compare two decimal numbers?
Is 0.700 greater than 0.7?
How do you use a number line to compare decimals?
What is the place value of the digit 3 in the decimal 0.639?
Can you compare decimals without a number line?
What happens if the whole number parts of the decimals are the same?
How many decimal places should you compare?
Why are decimals important in real life?

Comparing Decimals on a Number Line: Up to Thousandths exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the learning text Comparing Decimals on a Number Line: Up to Thousandths .
• What is a decimal number?

Hints

Think about a number that has a part before and after a dot (for example, 3.14).

The dot in a decimal number is called a decimal point, which separates the whole number from the fractional part.

Solution

A decimal number is a representation of numbers that include a whole number and a fractional part, separated by a decimal point.

The fractional part can extend to tenths, hundredths, thousandths, and beyond.

• Which of the following numbers is greater: 2.27 or 2.7?

Hints

If the numbers in the ones place are the same, the tenths place will tell us which number is larger.

Look at the digits to the right of the decimal point to compare which is bigger.

Solution

2.7 > 2.27.

Compare the whole number parts: Both numbers have the same whole number part, which is 2.

Compare the tenths place: In 2.27, the digit in the tenths place is 2. In 2.7, the digit in the tenths place is 7.

Since 7 > 2, 2.7 > 2.27.

• Compare the decimals 4.458 and 4.765 to identify where they go on the number line.

Hints

Start by comparing the digits in the tenths place if the ones place digits are the same.

Compare the tenths digits, 4 in 4.458 and 7 in 4.765.

Solution

4.765 > 4.458.

Compare the ones place: Both numbers have the same ones place, which is 4.

Compare the tenths place: In 4.458, the digit in the tenths place is 4. In 4.765, the digit in the tenths place is 7.

Since 7 > 4, 4.765 > 4.458.

• Place the following decimals in order from smallest to largest: 5.82, 5.801, 5.89.

Hints

Compare the digits from left to right, starting with the ones place.

If the digits in one place value are the same, move to the next place value to determine the order.

You could add a 0 to the end of 5.82 and 5.89 so they all have three digits after the decimal point to help with comparing.

Solution

The correct order is: 5.801, 5.82, 5.89.

Steps:

1. Compare ones place: All numbers start with 5, so they're the same.

2. Compare tenths place:

5.82 has an 8

5.801 has an 8

5.89 has an 8

3. Compare hundredths place:

5.82 has a 2

5.801 has a 0

5.89 has a 9

So, 0 is smallest, 2 is in the middle, and 9 is the largest.

You can stop comparing after step 3.

• You are comparing the lengths of two ribbons.

Hints

Compare the digits in the ones place first.

If they are the same, then compare the digits in the tenths place.

Look at the tenths place: compare 4 in 2.45 and 5 in 2.54.

Which one is greater?

Solution

The ribbon that is 2.54 meters long is longer.

• You are comparing the weights of four different fruits to find out which one is the heaviest.

Hints

Start by comparing the digits in the ones place, then move to the tenths, hundredths, and thousandths places step by step.

If the digits are the same, move to the next place value to determine the larger number.

Solution

The banana is the heaviest, with a weight of 0.176 kg.

Compare the tenths place:

• All fruits have the same tenths digit (1), so move to the next digit.
• Compare the hundredths place:
Apple: 7

Banana: 7

Kiwi: 6

Orange: 6

The banana and apple both have 7, but we need to check the next digit for both to be sure.

• Compare the thousandths place for Banana and Apple:
Banana: 6

Apple: 2

The banana has the larger thousandths digit (6 > 2).

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Comparing Decimals on a Number Line: Up to Thousandths
CCSS.MATH.CONTENT.5.NBT.A.3.B