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Decimal Fractions

Decimal fraction is a fraction, where denominator is a power of 10.

For example, 110\frac{{1}}{{10}}, 17100\frac{{17}}{{100}}, 31000\frac{{3}}{{1000}} are all decimal fractions.

Nice thing about decimal fractions is that they can be easily converted into decimal.

We already know, that dividing by 10, moves decimal point one position to the left.

In case of dividing by 100=102{100}={{10}}^{{2}}, we move decimal point 2 positions to the left.

Thus, 110=0.1\frac{{1}}{{10}}={0.1}, 17100=0.17\frac{{17}}{{100}}={0.17}, 31000=0.003\frac{{3}}{{1000}}={0.003}.

Exercise 1. Write 710\frac{{7}}{{10}} as fraction.

Answer: 710=0.7\frac{{7}}{{10}}={0.7}.

Next exercise.

Exercise 2. Write 0.56{0.56} as fraction.

Answer: 0.56=56×10−2=56100{0.56}={56}\times{{10}}^{{-{2}}}=\frac{{56}}{{100}}.

Next exercise.

Exercise 3. Write −2571000-\frac{{257}}{{1000}} as decimal.

Answer: −2571000=−0.257-\frac{{257}}{{1000}}=-{0.257}.