Express the following decimals into fraction form 0.2 2 0.1 =
The Correct Answer and Explanation is:
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Let’s convert the given decimals to fraction form:
Given:
- 0.2
- 2
- 0.1
Step-by-step Conversion:
- Convert 0.2 to a fraction: 0.2=2100.2 = \frac{2}{10}0.2=102 Simplify 210\frac{2}{10}102 by dividing both numerator and denominator by 2: 210=15\frac{2}{10} = \frac{1}{5}102=51
- Convert 2 to a fraction: Any whole number can be written as a fraction by putting it over 1: 2=212 = \frac{2}{1}2=12
- Convert 0.1 to a fraction: 0.1=1100.1 = \frac{1}{10}0.1=101
Final Answers in Fraction Form:
- 0.2 = 15\frac{1}{5}51
- 2 = 21\frac{2}{1}12
- 0.1 = 110\frac{1}{10}101
Explanation
Decimals are another way of expressing parts of a whole number. They are based on the powers of ten. Converting a decimal to a fraction means expressing it in terms of numerator and denominator where both are integers and the denominator is not zero.
To convert 0.2 to a fraction, consider that the digit 2 is in the tenths place. This means it is two-tenths. Mathematically, 0.2 is equal to 2 over 10, written as 210\frac{2}{10}102. However, this fraction is not in its simplest form. To simplify a fraction, we divide both the numerator and the denominator by their greatest common divisor. For 2 and 10, the greatest common divisor is 2. So dividing both by 2 gives us 15\frac{1}{5}51, which is the simplest form.
For the number 2, which is a whole number, we can write it as 21\frac{2}{1}12. This is because dividing any number by 1 gives the number itself. Writing whole numbers this way allows them to be used in operations involving fractions.
For 0.1, the digit 1 is in the tenths place, which makes it one-tenth. This is directly written as 110\frac{1}{10}101, and this is already in its simplest form.
Understanding how to express decimals as fractions helps in many areas of mathematics including algebra, ratios, and probability. It provides a clearer sense of proportion and makes comparison and computation easier, especially when working with different forms of numbers.
