We know how long in Earth days it takes for Mercury, Venus and Mars to orbit the Sun.

Mercury : Venus : Mars : 87 \frac{2 4}{2 5} 224 \frac{7}{1 0} 686 \frac{4 9}{5 0}

The given values are written as mixed numbers. We want to write them as a decimals. To rewrite a mixed number as a decimal, we follow two steps.

Write the mixed number as a sum of a whole number and a proper fraction.
Multiply the numerator and the denominator by a number that makes the new denominator a multiple of $10 .$

Let's rewrite one number at a time. To rewrite

87 \frac{2 4}{2 5},

we will start by writing it as a sum.

87 \frac{2 4}{2 5} = 87 + \frac{2 4}{2 5}

The denominator of

\frac{2 4}{2 5}

is

25 .

Because

25

times

4

is equal to

100,

we will expand the fraction by

4 .

87 + \frac{2 4}{2 5}

$\frac{a}{b} = \frac{a \cdot 4}{b \cdot 4}$

87 + \frac{2 4 \cdot 4}{2 5 \cdot 4}

87 + \frac{9 6}{1 0 0}

Write as a decimal

87 + 0.96

Add terms

87.96

We found that

87 \frac{2 4}{2 5}

is equal to

87.96 .

Next, let's rewrite

224 \frac{7}{1 0} .

We will start by writing

224 \frac{7}{1 0}

as a sum.

224 \frac{7}{1 0} = 224 + \frac{7}{1 0}

Since the denominator of

\frac{7}{1 0}

is

10,

we do not have to expand this fraction.

224 + \frac{7}{1 0}

Write as a decimal

224 + 0.7

Add terms

224.7

This means that

224.7

is equivalent to

224 \frac{7}{1 0} .

Finally, we convert the last mixed number,

686 \frac{4 9}{5 0} .

Let's write it as a sum.

686 \frac{4 9}{5 0} = 686 + \frac{4 9}{5 0}

The denominator of

\frac{4 9}{5 0}

is

50 .

Because

50

times

2

is equal to

100,

we will expand the fraction by

2 .

686 + \frac{4 9}{5 0}

$\frac{a}{b} = \frac{a \cdot 2}{b \cdot 2}$

686 + \frac{4 9 \cdot 2}{5 0 \cdot 2}

686 + \frac{9 8}{1 0 0}

Write as a decimal

686 + 0.98

Add terms

686.98

We wrote all the numbers as decimals!

Mercury : Venus : Mars : 87.96 224.7 686.98

Exercise