Question

What is the product of 8. 2 × 109 and 4. 5 × 10-5 in scientific notation? 36. 9 × 10-45 12. 7 × 104 3. 69 × 105 3. 69 × 1014.

Answer 1

When the two number has different power but the base is same, then to multiply them add their power keeping the base same.

The product of the given number is $3.69\times10^5$. Thus the option 3 is the correct option.

What is the exponent power with base 10?

To write the big number in short form, we write them in the positive power of 10.

To write the very small number, we write them in the negative power of 10.

How to multiply number with different power?

When the two number has different power but the base is same, then to multiply them add their power keeping the base same.

Given information-

The given number whose product has to find out are $8.2\times10^9$ and $4.5\times10^{-5}$ Let  be the product of the given number. thus,

Suppose the product of two number is x. Thus,

$x=(8.2\times10^9)\times(4.5\times10^{-5})$

Rearrange the equation as,

$x=8.2\times10^9\times4.5\times10^{-5}\\x=8.2\times4.5\times10^9\times10^{-5}$

As the base is same for 10 but power is different. Thus add the power to multiply them,

$x=(8.2\times4.5)\times(10^9\times10^{-5})\\x=36.9\times(10^{9-5})\\x=3.69\times10^1\times(10^4)\\x=3.69\times(10^{1+4})\\x=3.69\times10^5$

Hence the product of the given number is $3.69\times10^5$. Thus the option 3 is the correct option.

Learn more about the exponent power with base 10 here;

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