Write 1.42 as a fraction or mixed number in simplest form.
The correct answer and explanation is:
To write 1.42 as a fraction or mixed number in simplest form, follow these steps:
Step 1: Understand the number
1.42 is a decimal number. It can be written as a mixed number because it has a whole part (1) and a fractional part (0.42).
Step 2: Convert the decimal part to a fraction
The decimal part is 0.42.
- 0.42 means 42 hundredths, or 42100\frac{42}{100}.
Step 3: Simplify the fraction 42100\frac{42}{100}
To simplify 42100\frac{42}{100}, find the greatest common divisor (GCD) of 42 and 100.
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
- The greatest common factor is 2.
Divide numerator and denominator by 2: 42÷2100÷2=2150\frac{42 \div 2}{100 \div 2} = \frac{21}{50}
Step 4: Write the mixed number
Since the original number is 1.42, which is 1+0.421 + 0.42, we write it as: 121501 \frac{21}{50}
This is the mixed number form in simplest terms.
Step 5: Optional – write as an improper fraction
If you want the improper fraction form, convert the mixed number to an improper fraction: 12150=1×50+2150=50+2150=71501 \frac{21}{50} = \frac{1 \times 50 + 21}{50} = \frac{50 + 21}{50} = \frac{71}{50}
Final answers:
- Mixed number: 121501 \frac{21}{50}
- Improper fraction: 7150\frac{71}{50}
Explanation Summary (300 words):
Writing a decimal number like 1.42 as a fraction or mixed number involves converting the decimal portion into a fraction and then simplifying that fraction.
First, recognize that 1.42 consists of a whole number part (1) and a decimal part (0.42). The decimal part represents a fraction of a whole. Specifically, 0.42 means 42 parts out of 100, which can be written as 42100\frac{42}{100}.
The fraction 42100\frac{42}{100} is not in simplest form because both the numerator and denominator share a common factor. To simplify a fraction, you find the greatest common divisor (GCD) of both numbers. Here, 42 and 100 share a GCD of 2. Dividing both numerator and denominator by 2 reduces the fraction to 2150\frac{21}{50}.
Next, combine the whole number part with the simplified fraction to write the decimal as a mixed number: 121501 \frac{21}{50}.
If you prefer to write it as an improper fraction (a single fraction without a whole number part), multiply the whole number (1) by the denominator (50), add the numerator (21), and put the result over the original denominator. This gives 7150\frac{71}{50}.
Thus, 1.42 can be expressed as 121501 \frac{21}{50} in simplest mixed number form or 7150\frac{71}{50} as an improper fraction. Both are equivalent to the decimal 1.42.