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Convert the given common fractions to decimal fractions and leave your answer in 1dp.

Mathematics

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Here are the solutions to the problems.

Part 1: Convert the following decimals to common fractions.

a) 0.12

  1. Write the decimal as a fraction with a denominator of a power of 10.

    0.12=121000.12 = \frac{12}{100}
  2. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4.

    12÷4100÷4=325\frac{12 \div 4}{100 \div 4} = \frac{3}{25}

    The common fraction is 325\boxed{\frac{3}{25}}.

    b) 0.05

  3. Write the decimal as a fraction.

    0.05=51000.05 = \frac{5}{100}
  4. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5.

    5÷5100÷5=120\frac{5 \div 5}{100 \div 5} = \frac{1}{20}

    The common fraction is 120\boxed{\frac{1}{20}}.

    c) 0.9

  5. Write the decimal as a fraction.

    0.9=9100.9 = \frac{9}{10}
  6. The fraction is already in its simplest form.

    The common fraction is 910\boxed{\frac{9}{10}}.

    Part 2: Convert to decimal fraction and leave your answer in 1 dp.

    a) 23\frac{2}{3}

  7. Divide the numerator by the denominator.

    23=0.666...\frac{2}{3} = 0.666...
  8. Round to 1 decimal place.

    The second decimal place is 6, so we round up the first decimal place.

    0.666...≈0.70.666... \approx 0.7

    The decimal fraction to 1 dp is 0.7\boxed{0.7}.

    b) 29\frac{2}{9}

  9. Divide the numerator by the denominator.

    29=0.222...\frac{2}{9} = 0.222...
  10. Round to 1 decimal place.

    The second decimal place is 2, so we keep the first decimal place as it is.

    0.222...≈0.20.222... \approx 0.2

    The decimal fraction to 1 dp is 0.2\boxed{0.2}.

    c) 2142 \frac{1}{4}

  11. Convert the mixed number to a decimal.

    214=2+14=2+0.25=2.252 \frac{1}{4} = 2 + \frac{1}{4} = 2 + 0.25 = 2.25
  12. Round to 1 decimal place.

    The second decimal place is 5, so we round up the first decimal place.

    2.25≈2.32.25 \approx 2.3

    The decimal fraction to 1 dp is 2.3\boxed{2.3}.

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