Comparing and Ordering Decimals to Hundredths

Comparing decimals is very similar to comparing whole numbers. You just need to look carefully at the place value of each digit, starting from the left and moving to the right. We use the standard math symbols to show the relationship:

• $>$ means greater than
• $<$ means less than
• $=$ means equal to

How to Compare Two Decimals

To compare two decimal numbers, follow these simple steps:

1. Compare the whole numbers first (the numbers to the left of the decimal point). If one whole number is bigger, that entire decimal is larger.
2. Compare the tenths place. If the whole numbers are the same, look at the first digit to the right of the decimal point.
3. Compare the hundredths place. If the tenths are also the same, look at the second digit to the right of the decimal point.

Example: Compare $0.45$ and $0.39$

• Whole numbers: Both are $0$.
• Tenths place: $0.45$ has a $4$ in the tenths place. $0.39$ has a $3$ in the tenths place.
• Since $4$ tenths is greater than $3$ tenths ($4 > 3$), we know that $0.45 > 0.39$.

The Rule of Trailing Zeros

Adding a zero to the very end of a decimal (after the decimal point) does not change its value.

Example: Compare $3.6$ and $3.60$

• $3.6$ is three and six tenths.
• $3.60$ is three and sixty hundredths.
• Because $6$ tenths is exactly the same amount as $60$ hundredths, these numbers are perfectly equal.
• Therefore, $3.6 = 3.60$.

Ordering Decimals

When you need to put a list of decimals in order from least to greatest, the easiest trick is to line up the decimal points and add trailing zeros so they all have the same number of digits. This makes them much easier to compare!

Example: Order $0.7$, $0.65$, and $0.71$ from least to greatest.

1. Give them all the same number of decimal places by adding a trailing zero to $0.7$:
   • $0.7 \rightarrow 0.70$
   • $0.65 \rightarrow 0.65$
   • $0.71 \rightarrow 0.71$
2. Now look at the hundredths ($70$, $65$, and $71$).
3. The smallest is $0.65$, the next is $0.70$, and the largest is $0.71$.

The correct order from least to greatest is: $0.65$, $0.7$, $0.71$.