Question

29. Explain the Error A student found the product of 8 × 10 6 and 5 × 10 9 to be 4 × 10 15 . What is the error? What is the correct product?

Answer 1

`4 * 10^(16) or 40*10^(15)`

Explanation:

We are given that the student has found the product of two terms which is wrong and we have to find the correct one

Value 1:
`8 * 10^(6)`

Value 2:
`5*10^9`

Product of value1 and value 2:
`8*10^6 * 5*10^9 = 4 * 10^(15)`

which is wrong

Error in the product:

`8*10^6 * 5*10^9 = 4 * 10^(15)`

The answer with error has reduced the value by a power of 10.

They have made one of the following mistakes:

Either the product of 8*5 was written as 4 instead of 40

Or
`10^6 * 10^9` was calculated as
`10^(14) instead of 10^(15)` because
`40 * 10^(14)` becomes
`4 *10^ {15}`

Correct Product:

`8*10^6 * 5*10^9 = 40 * 10^(15)`

Using formula:
`x^a * x^b = x^a+b`

`10^6 * 10^9 = 10^(15)`

8*5 = 40

40 can be written as 4*10 and 10 is the same as
`10^1`

mulitplying them all

`4 * 10 ^ 1 * 10 ^6 * 10 ^9`

`= 4* 10^(16)`

which than becomes
`4 * 10^(16) or 40*10^(15)`