Lesson 2: Compare decimal fractions to the thousandths using like units, and express comparisons with >, <, =.

Property

To compare decimals, align them by their decimal points. Compare the digits in each place value, starting from the largest place (leftmost). The first place where the digits differ determines which number is greater.

Examples

Property

To compare decimals, rewrite them so they have the same number of decimal places (like units) by adding trailing zeros. This does not change the decimal's value. Once in like units, compare the numbers as if they were whole numbers. For example, to compare $0.5$ and $0.125$, rewrite $0.5$ as $0.500$.

Examples

Property

To compare fractions with denominators of 10, 100, or 1000, first write them in unit form. Then, convert them to have like units (a common denominator) before comparing their numerators. For example, to compare $\frac{a}{10}$ and $\frac{b}{100}$, rewrite $\frac{a}{10}$ as $\frac{10a}{100}$.

Examples

Compare $\frac{7}{10}$ and $\frac{34}{100}$.

• $\frac{7}{10}$ is 7 tenths. $\frac{34}{100}$ is 34 hundredths.
• 7 tenths = 70 hundredths.
• Since 70 hundredths > 34 hundredths, $\frac{7}{10} > \frac{34}{100}$.

Compare $\frac{4}{10}$ and $\frac{400}{1000}$.

• $\frac{4}{10}$ is 4 tenths. $\frac{400}{1000}$ is 400 thousandths.
• 4 tenths = 400 thousandths.
• Since 400 thousandths = 400 thousandths, $\frac{4}{10} = \frac{400}{1000}$.

Explanation

This skill connects fractions to their decimal unit equivalents. By expressing fractions like $\frac{7}{10}$ as "7 tenths" and $\frac{34}{100}$ as "34 hundredths", you can use place value understanding to compare them. To compare values accurately, you must first convert them to like units, such as changing tenths to hundredths. This method reinforces the relationship between fractions and decimals and strengthens comparison skills.