What is 4.2 as a fraction
The Correct Answer and Explanation is:
To express 4.2 as a fraction, follow these steps:
- Write the decimal as a fraction:
Begin by recognizing that 4.2 can be written as a mixed number. The whole number part is 4, and the decimal part is 0.2. So, we can write 4.2 as:
[
4.2 = 4 + 0.2
] - Convert the decimal part (0.2) into a fraction:
The decimal 0.2 is equivalent to 2 tenths, or ( \frac{2}{10} ). Thus, we have:
[
4.2 = 4 + \frac{2}{10}
] - Combine the whole number and the fraction:
To combine 4 and ( \frac{2}{10} ), we write 4 as ( \frac{40}{10} ) (since 4 is equivalent to ( \frac{40}{10} )). Now, we can add the two fractions:
[
4.2 = \frac{40}{10} + \frac{2}{10}
]
Since the denominators are the same, we simply add the numerators:
[
4.2 = \frac{40 + 2}{10} = \frac{42}{10}
] - Simplify the fraction:
The fraction ( \frac{42}{10} ) can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2. So, we divide both 42 and 10 by 2:
[
\frac{42}{10} = \frac{42 \div 2}{10 \div 2} = \frac{21}{5}
]
Therefore, 4.2 as a fraction is ( \frac{21}{5} ).
Explanation:
When converting a decimal to a fraction, it’s important to recognize the place value of the decimal. In this case, 4.2 has one decimal place, which means it can be expressed as ( \frac{2}{10} ). To combine this with the whole number 4, we convert 4 into a fraction with the same denominator, ( \frac{40}{10} ), and then add the fractions. The result is ( \frac{42}{10} ), which simplifies to ( \frac{21}{5} ). Simplification is necessary to present the fraction in its simplest form. This method can be applied to any decimal to convert it into a fraction.