Comparing, Ordering, and Rounding Decimals

Understanding how to compare, order, and round decimals is all about mastering place value. Whether you are dealing with tenths, hundredths, or thousandths, a few simple rules will help you find the right answer every time.

The Rule of Trailing Zeros

Before comparing decimals, it is important to know that adding zeros to the very end of a decimal does not change its value.

For example: $0.5 = 0.50 = 0.500$

This trick is incredibly helpful when comparing decimals of different lengths, as it allows you to easily line up their place values.

Comparing Decimals

To compare two decimals, examine the digits from left to right, starting with the largest place value (the whole numbers).

Example: Compare $0.089$ and $0.1$.

1. Line up the decimal points.
2. Add trailing zeros so both numbers have the same number of digits: compare $0.089$ to $0.100$.
3. Look at the tenths place: $0 < 1$.

Therefore, $0.1 > 0.089$.

Ordering Decimals

Ordering decimals follows the exact same process as comparing. You simply line them all up and compare the digits from left to right!

Example: Order $3.456$, $3.465$, and $3.546$ from least to greatest.

1. The ones digit ($3$) is the same for all three numbers.
2. Look at the tenths place: $3.456$ and $3.465$ have a $4$, but $3.546$ has a $5$. So, $3.546$ is the greatest.
3. Now compare the remaining two ($3.456$ and $3.465$). Look at the hundredths place: $5 < 6$. Therefore, $3.456 < 3.465$.

Final Order: $3.456$, $3.465$, $3.546$.

Rounding Decimals

Rounding decimals works just like rounding whole numbers.

1. Identify the target place you are rounding to (e.g., tenths or hundredths).
2. Look at the digit immediately to its right.
3. If it is $5$ or more, round up. If it is $4$ or less, keep the target digit the same.
4. Drop all digits to the right of your target place.

Example: Round $4.3672$ to the nearest hundredth.

• The digit in the hundredths place is $6$.
• The digit immediately to its right is $7$.
• Since $7$ is $5$ or more, we round up the $6$ to a $7$.
• Answer: $4.37$