# Comparing Decimals Using Place Value: Up to Thousandths

## Comparing Decimals using Place Value – Introduction

When we deal with numbers, each digit's position can dramatically change its value. This is especially true with decimal numbers, where the concept of place value becomes quite important. Understanding and comparing place value decimals is crucial, as it sets the foundation for mathematical precision and accuracy in real-world applications.

## Understanding Decimal Place Value – Definition

The place value of a decimal number determines the value of the digit based on its position relative to the decimal point. To the left of the decimal point are whole numbers, and to the right are fractional parts.

The further left a digit is, the greater its value. Moving rightwards from the decimal point, each place represents a fraction of a whole, decreasing in value by a factor of ten.

What is the value of the digit '7' in the number 6.307?
If you have the decimal 3.48, what does the '4' represent?

## Comparing Place Value Decimals – Example

Learning to compare decimals is like sizing up different objects to see which is heavier, longer, or taller. The same logic applies to numbers, where we compare place values to determine which decimal is greater, lesser, or if they are equal.

Here's how to compare two decimals:

• Step 1: Look at the whole number part before the decimal point. The larger whole number indicates a larger value.
• Step 2: Compare the digits after the decimal point starting with the Tenths place. If they are the same, move to the next place value.
• Step 3: Continue comparing digits until you find a place where the digits differ. The decimal with the larger digit in the smallest place value where they differ is the greater number.
Which is greater: 0.9 or 0.89?
Without using a number line, how would you know if 0.701 is larger than 0.72?

## Comparing Place Value Decimals – Guided Practice

Compare the decimals 0.564 and 0.568 to determine which is greater.
Which is greater: 0.372 or 0.38?
Which is greater: 0.703 or 0.71?
Compare the decimals 0.491 and 0.498 to determine which is greater.
Which is greater: 0.256 or 0.259?
Which is greater: 0.627 or 0.632?

## Comparing Place Value Decimals – Practice

Practice comparing decimals independently!

## Comparing Decimals using Place Value – Summary

Key Learnings from this Text:

• Decimal place value is essential for understanding the worth of numbers in different positions.

• To compare decimals, start with the whole number part, then move rightward, comparing digits until they differ.

• A place value chart is a helpful tool for visualizing and understanding decimals.

• Real-world applications of comparing decimals include financial literacy, measurements in science, and more.

## Comparing Decimals using Place Value – Frequently Asked Questions

Why is place value important when comparing decimals?
How do you use a place value chart to compare decimals?
What happens if the decimals have a different number of digits?
Can decimals with different whole numbers be equal?
How do zeros to the right of a decimal number affect its value?
What do you do if all the digits in the place value chart are the same?
Is it possible for a decimal with fewer digits to be greater than one with more digits?
When comparing decimals, do you need to write out all the place values?
What is a practical application of comparing decimals?
Why might students need to compare decimals to the thousandths place?

## Comparing Decimals Using Place Value: 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 Using Place Value: Up to Thousandths .
• ### What does the digit '4' represent in the decimal number 3.48?

Hints

The digit is directly to the right of the decimal point.

Each position to the right of the decimal point represents a fraction of ten, with the first position being tenths, and the second hundredths.

Imagine a similar number like 7.12.

The 1 represents one tenth.

Use this to help you find the value of 4 in 3.48.

Solution

The digit 4 in the decimal number 3.48 represents 4 tenths, or 0.4.

• ### Why is 1.5 greater than 1.49 when comparing their place values?

Hints

Look at the first digit after the decimal point in each number.

How do these digits compare?

Consider what the value of 1.5 would be if it was written with an extra zero to match the number of decimal places in 1.49.

What does this tell you about its size relative to 1.49?

Compare the two numbers.

Solution

1.5 is greater than 1.49 because when comparing decimals, the digits are compared place by place from left to right.

In the tenths place, 1.5 has a 5 whereas 1.49 has an 4.

Since 5 is greater than 4, 1.5 is greater than 1.49.

• ### If you were to compare 0.701 and 0.72, which decimal would be greater and why?

Hints

Add an extra zero to the end of 0.72 to compare it directly with 0.701.

Does this change the way you compare the two decimals?

What are the values in the hundredths place for each decimal?

Solution

0.72 is greater than 0.701 because in the hundredths place, 0.72 has a 2 while 0.701 has a 0, and since the hundredths place is the first place where they differ, the number with the higher digit in this place—0.72— is the greater decimal.

1: Align the decimals to compare them directly. Write them as 0.720 and 0.701 to make it easier to compare.

2: Compare the tenths place. Both numbers have 7 in the tenths place, so we move to the next position.

3: Compare the hundredths place. 0.72 has a 2 in the hundredths place, whereas 0.701 has a 0. Since 2 is greater than 0, 0.72 is greater than 0.701.

4: The thousandths place comparison is unnecessary in this context because the hundredths place already determined the greater value.

• ### Compare the decimal numbers 0.392, 0.398, and 0.39.

Hints

Check each decimal place starting from the tenths to the thousandths.

Where do you find the first difference among the digits?

Consider the significance of the thousandths place in deciding the largest number when the tenths and hundredths are the same for all numbers.

Consider adding a zero to the end of 0.39 to make it 0.390, which helps in directly comparing it with 0.392 and 0.398 in terms of the thousandths place.

Solution

In order from smallest to largest, the numbers are 0.39, 0.392, and 0.398.

Look at the Tenths Place: All the numbers have 3 in the tenths place, so they are the same here.

Check the Hundredths Place: They all have 9 in the hundredths place too, so we still can't decide which is bigger.

Move to the Thousandths Place: Here we see the difference! 0.39 doesn't have a thousandths place, so it's like 0.390. 0.392 has 2, and 0.398 has 8.

Find the Biggest and Smallest: Since 0 is less than 2, and 2 is less than 8, we know 0.39 is the smallest, 0.392 is in the middle, and 0.398 is the biggest.

• ### Which glass has more juice?

Hints

Remember, a higher number in the rightmost place you compare means a larger overall decimal value.

Compare the thousandths place.

Does the digit in glass A or glass B have a higher value?

Focus on the last digit of each decimal, as the first two digits are the same.

Solution

Glass B has more juice.

Compare the Tenths Place: Look at the tenths digit of each decimal. Both 0.256 and 0.259 have 2 in the tenths place.

Compare the Hundredths Place: Both decimals have 5 in the hundredths place, so we still need to find a difference.

Compare the Thousandths Place: The thousandths place shows 6 for glass A and 9 for glass B.

Determine the Larger Amount: Since 9 is greater than 6, glass B has more juice.

• ### Apply your knowledge of comparing place value to compare numbers between zero and one.

Hints

Look at the last digit (thousandths place) of each decimal rate to determine which one is highest, as the tenths and hundredths places are the same for all options.

Remember, even a small difference in the rightmost decimal place can determine which option allows for a greater flow rate.

Focus on comparing these smallest differences.

Solution

The setting with 0.627 liters per minute will provide the most water flow over one minute.

Identify Decimal Places: Look at each number to recognize the digits in the tenths, hundredths, and thousandths places.

Compare the Tenths Place: All three settings have 6 in the tenths place, so no difference here.

Compare the Hundredths Place: The hundredths digits are 2 for 0.622, 2 for 0.625, and 2 for 0.627, so they are the same up to this point.

Compare the Thousandths Place: 0.622 has 2, 0.625 has 5, and 0.627 has 7. The setting with 7 in the thousandths place, which is 0.627, provides the most flow rate as it is the highest number in the smallest place value compared.

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Comparing Decimals Using Place Value: Up to Thousandths
CCSS.MATH.CONTENT.5.NBT.A.3.B