Decimal Comparison: Finding the Maximum Value of 0.709

Q: Why do I add zeros to the end of shorter decimals?

Adding trailing zeros doesn't change the value but helps you compare place by place! $ 0.71 = 0.710 $, so now you can easily see that $ 0.710 > 0.709 $.

Q: What if two decimals look very similar like 0.709 and 0.71?

Line them up by place value and add zeros: $ 0.709 $ vs $ 0.710 $. Now compare the thousandths place: 9 vs 0, so $ 0.71 $ is larger!

Q: How do I know which decimal place to look at first?

Always start from the leftmost place after the decimal point! Compare tenths first, then hundredths, then thousandths. Stop when you find different digits.

Q: Can I just ignore the zeros at the end?

Yes for the final answer, but not during comparison! $ 0.71 $ and $ 0.710 $ are equal, but you need the zero to compare with $ 0.709 $.

Q: What if I get confused about which number is bigger?

Try the number line trick! The decimal closer to 1 is larger. Or convert to fractions: $ 0.71 = \frac{71}{100} $ vs $ 0.709 = \frac{709}{1000} $.

Decimal Comparison with Place Value Analysis

Determine which of the following numbers is greater than $0.709$ :

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the larger number than the given number

00:03 We can always add 0 to the right side of the last digit:

00:07 Let's compare the digits of the numbers

00:11 The digit 1 is greater than 0, so the number is larger

00:18 Let's check the next number, using the same method

00:22 The digit 6 is less than 7, so the number is smaller

00:26 Let's check the next number, using the same method

00:35 The digit 1 is less than 9, so the number is smaller

00:40 Let's check the next number, using the same method

00:50 The digit 0 is less than 9, so the number is smaller

00:55 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Determine which of the following numbers is greater than $0.709$ :

Step-by-step solution

In order to determine the correct answer, let's proceed to compare the answers to the number and determine which is larger:

0.71 - By adding another 0 we are able compare 0.709 and 0.710. Given that the hundredths digit is 1 and 1 is greater than 0, this is the correct answer.

0.69 - Once again add another 0 to compare 0.709 and 0.690. Since the tenths digit is 6 and 6 is less than 0, this is not the correct answer.

0.70 - We'll add another 0 to compare 0.709 and 0.700. Due to the fact that the thousandths digit is 0 and 0 is less than 9, this is not the correct answer.

0.7 - Add two zeros to compare 0.709 and 0.700. Since the thousandths digit is 0 and 0 is less than 9, this is not the correct answer.

Final Answer

$0.71$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Compare digits from left to right position by position
Technique: Add trailing zeros to make equal lengths: $0.709$ vs $0.710$
Check: Verify by examining each decimal place: tenths, hundredths, then thousandths ✓

Common Mistakes

Avoid these frequent errors

Comparing decimal length instead of place values
Don't assume longer decimals are automatically larger like $0.709 > 0.71$ = wrong answer! Length doesn't determine size in decimals. Always align place values and compare digit by digit from left to right.

Practice Quiz

Test your knowledge with interactive questions

Are they the same numbers?

$0.1\stackrel{?}{=}0.10$

FAQ

Everything you need to know about this question

Why do I add zeros to the end of shorter decimals?

Adding trailing zeros doesn't change the value but helps you compare place by place! $0.71 = 0.710$ , so now you can easily see that $0.710 > 0.709$ .

What if two decimals look very similar like 0.709 and 0.71?

Line them up by place value and add zeros: $0.709$ vs $0.710$ . Now compare the thousandths place: 9 vs 0, so $0.71$ is larger!

How do I know which decimal place to look at first?

Always start from the leftmost place after the decimal point! Compare tenths first, then hundredths, then thousandths. Stop when you find different digits.

Can I just ignore the zeros at the end?

Yes for the final answer, but not during comparison! $0.71$ and $0.710$ are equal, but you need the zero to compare with $0.709$ .

What if I get confused about which number is bigger?

Try the number line trick! The decimal closer to 1 is larger. Or convert to fractions: $0.71 = \frac{71}{100}$ vs $0.709 = \frac{709}{1000}$ .

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