Why do you multiply by a power of 10 when writing a repeating decimal as a rational number

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Kyrobi Kyrobi

06-09-2017
Mathematics

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Why do you multiply by a power of 10 when writing a repeating decimal as a rational number

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smarazazaidi smarazazaidi · Answer 1 · 2019-09-01T20:40:49+02:00

The easy way to do this question is that if we move the point to right we take the ten’s power with negative sign and when we move point to left we tak ten’s power with positive number but the numbers we move taken as power

Further Explanation:

For Example:

You will understand all this procedure by following these simple steps that are as follows:

Suppose we have a number 5.2244

If we write it in notation form then we take its ten’s power to the 4 times with negative sign because we move the point to the right side

Solution:

Sol.

= 5 . 2 2 4 4

= 5 2 2 4 4 x 10 ^ -4.

2nd example:

If we have a number 8965.77

Sol.

= 8 9 6 5 . 7 7

= 8 . 9 6 5 7 7 x 10 ^ 3

Same as it I asked you that if we move towars left then we take the power of ten as positive. Hope you understand my opinion. I made it as easy as I can hope you understand all the topic.

Answer Details:

Subject: Mathematics

Level: High School.

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saimaparvezVT saimaparvezVT · Answer 2 · 2022-07-23T10:45:15+02:00

We would like to take a repeating decimal and express it as a quotient of two whole numbers.

What is standard form?

Standard form is a way of writing down in easy form of very large or very small numbers.

The idea is to multiply by some number (10, 100, 1000, etc.) so that when we subtract the original number from the multiple, the repeating part cancels out. If we multiply by 10, we get 10x = 2.

So, we multiply by a power of 10 when writing a repeating decimal as a rational number.

Learn more about Standard form

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