Question

write the following rational numbers in decimal form: -5/8​

Answer 1

Answer:

-0.625

Step-by-step explanation:

hope it's helpful

Answer 2

Step-by-step explanation:

Given: $-\frac{5}{8}$

To find: Write the given rational numbers in decimal form.

Solution:

Step 1: Write denominator in terms of ${2}^{n} \times {5}^{m}$

$-\frac{5}{8} = -\frac{5}{ {2}^{3} }$

Step 2: Multiply and divide by ${5}^{3}$

$-\frac{5}{8} = -\frac{5 \times 5^{3}}{5^3 \times 2^3}$

or

$-\frac{5}{8}= -\frac{5^4}{(5\times 2)^3}$

$-\frac{5}{8}= -\frac{625}{(10)^3}$

$-\frac{5}{8}= -\frac{625}{1000}$

Step 3: Write the decimal form.

$-\frac{5}{8} =-\frac{625}{1000} = -0.625$

Extra information:

When a rational number have denominator in the form ${2}^{n} \times {5}^{m}$, here n and m are positive integers, then the rational number have terminating decimal expansion.

After identification, make the powers of 2 and 5 same, so that without actual division we can find decimal form of the number.

Final answer:

$\bf -\frac{5}{8} = -0.625$

Hope it helps you.

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