Express the following in fraction form.
6. [tex]0.27[/tex]
[Sol] [tex]0.27 = \boxed{\frac{27}{100}}[/tex]
7. [tex]1.125[/tex]
[Sol] Set aside the whole number 1. Change [tex]0.125[/tex] into a fraction.
[tex]0.125=\frac{125}{1000}\\=\frac{125}{1000}\div \frac{25}{25}\\=\frac{5}{40}\\=\frac{1}{8}[/tex]
Bring back 1.
[tex]1.125=\boxed{1 \frac{1}{8}}[/tex]
8. [tex]0.2525...[/tex]
[Sol] Let [tex]x[/tex] be [tex]0.2525[/tex]. The repeating digit is [tex]25[/tex]. Move the decimal point two places to the right.
[tex]25.2525[/tex]
Then,
[tex]100x=25.2525\\100x-x=25.2525-0.2525\\99x=25\\x=\frac{25}{99}[/tex]
Therefore, [tex]0.2525=\boxed{\frac{25}{99}}[/tex].
9. [tex]3.7...[/tex]
[Sol] Set aside [tex]3[/tex]. Change [tex]0.7...[/tex] into a fraction. Let [tex]x[/tex] be [tex]0.7777[/tex]. The repeating digit is [tex]7[/tex]. Move the decimal point one place to the right.
[tex]7.7777[/tex]
Then,
[tex]10x=7.7777\\10x-x=7.7777-0.7777\\9x=7\\x=\frac{7}{9}[/tex]
Bring back [tex]3[/tex].
[tex]3.7... = \boxed{3 \frac{7}{9}}[/tex]
10. [tex]12.125[/tex]
[Sol] Set aside [tex]12[/tex]. Change [tex]0.125[/tex] into a fraction.
[tex]0.125=\frac{125}{1000}\\=\frac{125}{1000}\div \frac{25}{25}\\=\frac{5}{40}\\=\frac{1}{8}[/tex]
Bring back [tex]12[/tex].
[tex]12.125=\boxed{12 \frac{1}{8}}[/tex]
11. [tex]-3.6[/tex]
[Sol] Set aside [tex]-3[/tex]. Change [tex]0.6[/tex] into a fraction.
[tex]0.6=\frac{6}{10}\\=\frac{6}{10}\div \frac{2}{2}\\=\frac{3}{5}[/tex]
Bring back [tex]-3[/tex].
[tex]-3.6=\boxed{-3\frac{3}{5}}[/tex]
12. [tex]-24.7...[/tex]
[Sol] Set aside [tex]-24[/tex]. Change [tex]0.7...[/tex] into a fraction. Let [tex]x[/tex] be [tex]0.7777[/tex]. The repeating digit is [tex]7[/tex]. Move the decimal point one place to the right.
[tex]7.7777[/tex]
Then,
[tex]10x=7.7777\\10x-x=7.7777-0.7777\\9x=7\\x=\frac{7}{9}[/tex]
Bring back [tex]-24[/tex].
[tex]-24.7...=\boxed{-24\frac{7}{9}}[/tex]
Happy learning!
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