**Middle School Number Sense Lesson 7: Converting Decimals to Fractions**

**This basic concept appeared on**

**13 out of 15**middle school tests this year--8 times as question #6, 3 times as question #5, once as question #3, and once as question #11. So needless to say, this concept is important. Mastery will help you get past the first 10 questions and on to something that deserves a bit more of your time.

**Number Dojo Level: 29**

**Background**

If you have read my post from yesterday, you are already familiar with how to do this conversion backwards (going from decimals to fractions). In my opinion, this one is quite a bit easier. Decimals are basically fractional representations where the numerator consists of the number without the decimal, and the denominator is some power of 10. Specifically, that power of 10 happens to be the same as the # of digits to the right of the decimal. Confused? Allow me to demonstrate:

Take the decimal 0.41 for example. Since you know your place values already, you will know that the 4 represents 4 tenths, and the 1 represents 1 hundredth. Add those together (4 tenths = 40 hundredths), and you get

**41 hundredths**. This is shown in fractional form as

**41/100**. Notice that the numerator is the same as the number without the decimal, and the denominator is 10 to the power of 2 (or 1 with 2 zeros after it).

**Steps to convert a decimal to a fraction**

- Think of the number (without the decimal) as the numerator.
- How many digits are to the right of the decimal? Place that same # of zeros after a 1 for the denominator.
- Reduce the fraction.

**Example 1: 0.8 = ___ (fraction)**

**8**is your numerator.**10**is your denominator.- 8/10 reduces to
**4/5**.

**Example 2: 0.35 = ___ (fraction)**

**35**is your numerator.**100**is your denominator.- 35/100 reduces to
**7/20**.

**Example 3: 0.875 = ___ (fraction)**

**875**is your numerator.**1000**is your denominator.- 875 & 1000 are both divisible by 125. 875/1000 reduces to
**7/8**.

**Example 4: 1.25 = ___ (fraction)**

- (For decimals greater than 1, you still leave all the digits as the numerator as long as you remove the decimal.) So
**125**is your numerator. **100**is your denominator.- 125/100 reduces to
**5/4**.

**Example 4 (redo): 1.25 = ___ (fraction)**

- (It may be easier to ignore the # to the left of the decimal for this step, and then add it to the front of your fractional answer to make a mixed number).
**25**is your numerator. **100**is your denominator.- 25/100 reduces to 1/4. Add the 1 to make
**1 1/4**.

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

convdecifrac.pdf |

**Up Next for Middle School: OrderOfOper2**