Comparing Decimals
Comparing decimals means determining which decimal number is greater, lesser, or equal by examining place value from left to right. Align the decimal points and add trailing zeros so both numbers have the same number of decimal places. For example, 0.12 vs 0.012 becomes 0.120 vs 0.012, and since 120 thousandths is greater than 12 thousandths, 0.12 > 0.012. Terminal zeros like in 0.4 and 0.400 do not change the value. This skill appears in Chapter 4 of Saxon Math Course 2 and is essential for 7th grade math ordering and number sense.
Key Concepts
Property When comparing decimal numbers, it is necessary to consider place value. Aligning decimal points can help to compare decimal numbers digit by digit. It may be helpful to insert terminal zeros so that both numbers will have the same number of digits to the right of the decimal point, since terminal zeros do not add value.
Examples Compare $0.12$ and $0.012$. We add a zero to the first number to get $0.120$. Since $120$ thousandths is greater than $12$ thousandths, we know $0.12 0.012$. Compare $0.4$ and $0.400$. Since terminal zeros don't change the value, we can see that $0.4 = 0.400$. Compare $1.1$ and $1.099$. We can add two zeros to the first number to get $1.100$. Since $1.100$ is greater than $1.099$, we have $1.1 1.099$.
Explanation Think of it like a Wild West duel! To see which decimal is bigger, line up their decimal points. If needed, add zeros to the end of one number so they both have the same number of digits. Now, compare them from left to right, place by place, to declare the undisputed champion of value!
Common Questions
How do you compare two decimal numbers?
Align the decimal points, add trailing zeros to equalize the number of digits, then compare digit by digit from left to right. The first position where they differ determines which is greater.
Does adding a zero to the end of a decimal change its value?
No. Terminal zeros after the last nonzero digit do not change the value. 0.4, 0.40, and 0.400 are all equal.
How do you compare 0.12 and 0.012?
Write them with the same number of decimal places: 0.120 and 0.012. Compare the tenths place: 1 > 0, so 0.12 > 0.012.
What are common mistakes when comparing decimals?
Students often assume the decimal with more digits is larger. For example, they might think 0.012 > 0.12 because it has more digits, but place-value comparison shows the opposite.
Why is comparing decimals important?
Comparing decimals is essential for ordering data, making purchasing decisions, interpreting measurements, and solving inequalities in algebra.
Is comparing decimals covered in 7th grade?
Yes. Saxon Math Course 2 teaches decimal comparison in Chapter 4, reinforcing place-value understanding as students work with more complex decimal operations.