QuestionLesson 4-1
Rational Numbers
Write each fraction as a decimal. Determine if the decimal is a terminating decimal. (Examples 1 and 2)
1.
2.
3.
Studdy Solution
STEP 1
1. A rational number can be expressed as a fraction , where and are integers and .
2. A terminating decimal is a decimal that has a finite number of digits after the decimal point.
3. To determine if a fraction is a terminating decimal, the denominator (in its simplest form) should only have the prime factors 2 and/or 5.
STEP 2
1. Convert each fraction to a decimal.
2. Determine if the decimal is terminating.
STEP 3
Convert to a decimal by performing the division .
STEP 4
Determine if is a terminating decimal.
- The denominator can be factored into .
- Since the only prime factor is 2, is a terminating decimal.
STEP 5
Convert to a decimal by performing the division .
STEP 6
Determine if is a terminating decimal.
- The denominator is already a prime number.
- Since the only prime factor is 5, is a terminating decimal.
STEP 7
Convert to a decimal by performing the division .
STEP 8
Determine if is a terminating decimal.
- The denominator is already a prime number.
- Since the only prime factor is 5, is a terminating decimal.
The decimals for the fractions are:
1. , which is a terminating decimal.
2. , which is a terminating decimal.
3. , which is a terminating decimal.
Was this helpful?