How to convert the following decimals into a fraction?
0.44
The first digit to the right of the decimal is the tenths digit, and the second digit is the hundredths digit. It can be written as follows:
0.44 = \dfrac{4}{10}+ \dfrac{4}{100} = \dfrac{40+4}{100}= \dfrac{44}{100}
Notice that:
\dfrac{44}{100}= \dfrac{4\times11}{4\times25}
Therefore:
0.44=\dfrac{11}{25}
0.136
The first digit to the right of the decimal is the tenths digit, the second digit is the hundredths digit, and the third digit is the thousandths digit. It can be written as follows:
0.136 = \dfrac{1}{10}+ \dfrac{3}{100} + \dfrac{6}{1\ 000} = \dfrac{100+30+6}{1\ 000}= \dfrac{136}{1\ 000}
Notice that:
\dfrac{136}{1\ 000}= \dfrac{8\times17}{8\times125}
Therefore:
0.136=\dfrac{17}{125}
2.25
The first digit to the right of the decimal is the tenths digit, and the second digit is the hundredths digit. It can be written as follows:
2.25 = 2+ \dfrac{2}{10}+ \dfrac{5}{100} = \dfrac{200+20+5}{100}= \dfrac{225}{100}
Notice that:
\dfrac{225}{100}= \dfrac{25\times9}{25\times4}
Therefore:
2.25= \dfrac{9}{4}
0.05
The first digit to the right of the decimal is the tenths digit, and the second digit is the hundredths digit. It can be written as follows:
0.02 = \dfrac{0}{10}+ \dfrac{2}{100} = \dfrac{2}{100}
Notice that:
\dfrac{2}{100}= \dfrac{2\times1}{2\times50}
Therefore:
0.02=\dfrac{1}{50}
1.025
The first digit to the right of the decimal is the tenths digit, the second digit is the hundredths digit, and the third digit is the thousandths digit. It can be written as follows:
1.025 = 1+\dfrac{0}{10}+ \dfrac{2}{100} + \dfrac{5}{1\ 000} = \dfrac{1\ 000+20+5}{1\ 000}= \dfrac{1\ 025}{1\ 000}
Notice that:
\dfrac{1\ 025}{1\ 000}= \dfrac{25\times41}{25\times40}
Therefore:
1.025=\dfrac{41}{40}
0.875
The first digit to the right of the decimal is the tenths digit, the second digit is the hundredths digit, and the third digit is the thousandths digit. It can be written as follows:
0.875 = \dfrac{8}{10}+ \dfrac{7}{100} + \dfrac{5}{1\ 000} = \dfrac{800+70+5}{1\ 000}= \dfrac{875}{1\ 000}
Notice that:
\dfrac{875}{1\ 000}= \dfrac{125\times7}{125\times 8}
Therefore:
0.875=\dfrac{7}{8}
2.208
The first digit to the right of the decimal is the tenths digit, the second digit is the hundredths digit, and the third digit is the thousandths digit. It can be written as follows:
2.208 = 2+\dfrac{2}{10}+ \dfrac{0}{100} + \dfrac{8}{1\ 000} = \dfrac{2\ 000+200+8}{1\ 000}= \dfrac{2\ 208}{1\ 000}
Notice that:
\dfrac{2\ 208}{1\ 000}= \dfrac{8\times276}{8\times125}
Therefore:
2.208=\dfrac{276}{125}