How to Convert Decimals to Fractions by Dividing by Prime Numbers

Let’s walk through how to convert decimals to fractions by dividing by prime numbers, using a few examples.

Write the Decimal as a Fraction
Start by writing 0.6 as a fraction: 0.6 becomes 6/10.
Simplify the Fraction
- Divide both the numerator (6) and the denominator (10) by the smallest prime number, which is 2: 6 divided by 2 is 3, and 10 divided by 2 is 5. So, 6/10 simplifies to 3/5.
- Since 3 and 5 are prime numbers and cannot be simplified further, the fraction is already in its simplest form.
Thus, 0.6 as a fraction is 3/5.

Write the Decimal as a Fraction
Write 0.75 as a fraction: 0.75 becomes 75/100.
Simplify the Fraction
- Start by dividing both the numerator (75) and the denominator (100) by 5: 75 divided by 5 is 15, and 100 divided by 5 is 20. So, 75/100 simplifies to 15/20.
- Divide again by 5: 15 divided by 5 is 3, and 20 divided by 5 is 4. So, 15/20 simplifies to 3/4.
- Since 3 and 4 cannot be simplified further, the fraction is in its simplest form.
Thus, 0.75 as a fraction is 3/4.

Write the Decimal as a Fraction
Write 0.125 as a fraction: 0.125 becomes 125/1000.
Simplify the Fraction
- Divide both the numerator (125) and the denominator (1000) by 5: 125 divided by 5 is 25, and 1000 divided by 5 is 200. So, 125/1000 simplifies to 25/200.
- Divide again by 5: 25 divided by 5 is 5, and 200 divided by 5 is 40. So, 25/200 simplifies to 5/40.
- Divide once more by 5: 5 divided by 5 is 1, and 40 divided by 5 is 8. So, 5/40 simplifies to 1/8.
- Since 1 is a prime number and 8 cannot be simplified further, the fraction is in its simplest form.
Thus, 0.125 as a fraction is 1/8.

To convert a decimal to a fraction using prime numbers:

Write the decimal as a fraction.
Divide the numerator and denominator by the smallest prime numbers repeatedly until you can’t simplify further.
Ensure the fraction is in its simplest form.

This method will help you convert decimals to their simplest fraction form easily!

Evaluation

0.5 can be written as the fraction __________. a) 1/2 b) 2/5 c) 5/10 d) 1/5
To convert 0.4 to a fraction, you write it as __________. a) 4/10 b) 2/5 c) 4/20 d) 1/4
0.25 can be expressed as the fraction __________. a) 1/4 b) 2/5 c) 1/5 d) 2/8
To simplify 0.75 written as 75/100, you first divide by __________. a) 2 b) 3 c) 5 d) 10
The fraction for 0.6 in simplest form is __________. a) 1/2 b) 3/5 c) 2/3 d) 6/10
0.125 can be simplified to the fraction __________. a) 1/8 b) 1/4 c) 1/10 d) 5/40
To convert 0.8 to a fraction, write it as __________. a) 4/5 b) 2/5 c) 8/10 d) 4/10
The decimal 0.2 written as a fraction is __________. a) 1/5 b) 2/10 c) 1/2 d) 2/5
To simplify the fraction 10/100 from the decimal 0.1, you divide by __________. a) 10 b) 2 c) 5 d) 20
The decimal 0.9 as a fraction is __________. a) 9/10 b) 1/9 c) 3/4 d) 9/100
Converting 0.03 to a fraction results in __________. a) 3/100 b) 1/3 c) 3/10 d) 1/10
The fraction for 0.7 in its simplest form is __________. a) 7/10 b) 1/7 c) 1/10 d) 7/100
To simplify 0.12 written as 12/100, you divide by __________. a) 4 b) 6 c) 3 d) 2
The decimal 0.05 converted to a fraction is __________. a) 1/20 b) 5/100 c) 1/50 d) 5/10
The simplest form of the fraction for 0.4 is __________. a) 2/5 b) 4/10 c) 1/4 d) 1/5

These questions should help reinforce understanding of converting decimals to fractions and simplifying them.

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