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Convert the following decimals to common fractions in their simplest form: a) 0.26 b) 0.08 c) 0.43 d) 0.25

Mathematics

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1. Write as common fractions in their simplest form:

*a) 0,26

  1. Write the decimal as a fraction with a denominator of 100.

    0,26=261000,26 = \frac{26}{100}

  2. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2.

    26÷2100÷2=1350\frac{26 \div 2}{100 \div 2} = \frac{13}{50}

    The common fraction in simplest form is: 1350\boxed{\frac{13}{50}}

    *b) 0,08

  3. Write the decimal as a fraction with a denominator of 100.

    0,08=81000,08 = \frac{8}{100}

  4. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4.

    8÷4100÷4=225\frac{8 \div 4}{100 \div 4} = \frac{2}{25}

    The common fraction in simplest form is: 225\boxed{\frac{2}{25}}

    *c) 0,43

  5. Write the decimal as a fraction with a denominator of 100.

    0,43=431000,43 = \frac{43}{100}

  6. The fraction cannot be simplified further as 43 is a prime number and 100 is not a multiple of 43.

    The common fraction in simplest form is: 43100\boxed{\frac{43}{100}}

    *d) 0,25

  7. Write the decimal as a fraction with a denominator of 100.

    0,25=251000,25 = \frac{25}{100}

  8. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 25.

    25÷25100÷25=14\frac{25 \div 25}{100 \div 25} = \frac{1}{4}

    The common fraction in simplest form is: 14\boxed{\frac{1}{4}}

    2. Write the following decimal numbers as percentages:

    *a) 0,4

  9. To convert a decimal to a percentage, multiply by 100%100\%.

    0,4×100%=40%0,4 \times 100\% = 40\%

    The percentage is: 40%\boxed{40\%}

    *b) 0,23

  10. To convert a decimal to a percentage, multiply by 100%100\%.

    0,23×100%=23%0,23 \times 100\% = 23\%

    The percentage is: 23%\boxed{23\%}

    3. Write the following common fractions as decimal fractions:

    *a) 1750\frac{17}{50}

  11. Convert the fraction to an equivalent fraction with a denominator of 100.

    Multiply the numerator and denominator by 2.

    1750=17×250×2=34100\frac{17}{50} = \frac{17 \times 2}{50 \times 2} = \frac{34}{100}

  12. Convert the fraction with denominator 100 to a decimal.

    34100=0,34\frac{34}{100} = 0,34

    The decimal fraction is: 0,34\boxed{0,34}

    *b) 1320\frac{13}{20}

  13. Convert the fraction to an equivalent fraction with a denominator of 100.

    Multiply the numerator and denominator by 5.

    1320=13×520×5=65100\frac{13}{20} = \frac{13 \times 5}{20 \times 5} = \frac{65}{100}

  14. Convert the fraction with denominator 100 to a decimal.

    65100=0,65\frac{65}{100} = 0,65

    The decimal fraction is: 0,65\boxed{0,65}

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