**High School Number Sense Lesson 16: Comparing Decimals and Fractions**

Sometimes you are given a decimal and a fraction, and you need to determine which is larger (or smaller). It is very helpful to have a working knowledge of common fractions and their decimal equivalents. I have created some free flashcards to help with this--found on the Worksheets tab of this site.

This concept showed up

**7 times**this year: most of the time at either

**question # 15 or 18**, but sometimes as early as question # 6.

**Number Dojo Level: 109**

The easiest way to solve these problems is usually to convert the fraction to a decimal--covered in my ConvFracDeci post. Then you can easily see which is larger (or smaller). For the most part, the fractions will have a denominator less than or equal to 16--the variations of which are covered in my flashcards.

**Example 1: Which is smaller, .75 or 7/9?**

- Convert the fraction to a decimal. 7/9 = 0.777...
- Compare the two decimals to pick the smaller one.
**.75**< .777...

**Example 2: Which is larger, 3/11 or .26?**

- Convert the fraction to a decimal. 3/11 = .2727...
- Compare the two decimals to pick the larger one. .2727... > .26, so
**3/11**is your answer.

**Example 3: Which is smaller, 3/8 or .38?**

- Convert the fraction to a decimal. 3/8 = .375
- Compare the two decimals to pick the smaller one. .375 < .38, so
**3/8**is your answer.

**Example 4: Which is larger, 4/17 or .25?**

- Convert the fraction to a decimal...except that's not easy. In this case, it is easier to convert the decimal to a fraction. .25 = 1/4 or 4/16.
- Compare the two fractions to pick the larger one. 4/16 is larger than 4/17 because it has the same numerator but a smaller denominator. So
**.25**is your answer.

**Example 5: Which is smaller, -.44 or -4/9?**

- Convert the fraction to a decimal. -4/9 = -.444...
- Compare the two decimals to pick the smaller one. -.444... < -.44, so
**-4/9**is your answer.

**Here's a free worksheet to help you practice CompareDeciF:**

comparedecif.pdf |

**Up Next for High School: RomanToArabic**