Question

How do you write $360\times {{10}^{-4}}$ in standard form ?

Answer 1

Hint: While writing a number in standard form when we the number is multiplied with ${{10}^{n}}$ where n is an integer we just shift the decimal sign n places towards right. When multiplied by ${{10}^{-n}}$ we shift the decimal sign n places towards the left. For example we if we multiply abc.def with ${{10}^{2}}$ the answer would be abcde.f and if we multiply with ${{10}^{-2}}$ we will get a.bcdef , where a, b, c, d and e are digits.

Complete step-by-step answer:
The given number is $360\times {{10}^{-4}}$
We can see that 360 is multiplied with ${{10}^{-4}}$ so we should shift the decimal sign 4 places towards left
We can write 360 as 00360.00
If we shift the decimal sign 4 places left 0.0360
So the standard form of $360\times {{10}^{-4}}$ is 0.0360

Note: When we convert a fraction into decimal we just write the whole number in the numerator without decimal sign and 10 to the power number of digits after the decimal sign in the denominator. For example if we have a decimal number abc.cd where a, b, c, d and e. we can see there are 2 digits after the decimal sign. So we can write abc.de as $\dfrac{abcde}{100}$. But we can write irrational numbers into fraction because irrational numbers are non- repetitive infinitely long decimal numbers. For example we can not write $\pi $ as a fraction, remember $\dfrac{22}{7}$ is an approximate value of $\pi $ not exact value of $\pi $ .