Explain how to multiply decimals by powers of 10. Use 8.653 x 10000 as an example, to show how the multiplication is done.

We move the decimal point to the right by a number of digit places equal to  the power of 10.

Step-by-step explanation:

If we want to multiply a decimal by a power of 10, we move the decimal point to the right by a number of digit places which is the power of the number ten or the number of zeros which are present in the multiplying number 10. If we do not have a digit after the last digit, we put zeros to complete the number of digits until, we have the number of digit places added after the decimal point which are equal to the power of 10.

Using the example given above

8.653 x 10000, we have four zeros. So, in index form it is

8.653 x 10⁴

Since we have the number 10 raised to the power of four or having 4 zeros, we move the decimal point 4 places to the right.

So, 8.653 x 10000 = 8.653 x 10⁴ = 86530

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