Question

Peter is writing a number in scientific notation.The number is grater that ten million and less that one hundred million.Which exponent will peter use?

Answer 1

`M = a * 10^7` where 1 < a ≤ 9

The EXPONENT USED BY PETER is 7 in all the possible cases.

Explanation:

Let us assume the needed number is M.

Also, given:

The needed number is GREATER than 10 Million.

⇒ M > 10 Million

⇒ M > 10,000,000

⇒ M >
`1 * 10^7` ...... (1)

The needed number is SMALLER than 100 Million.

⇒ M < 100 Million

⇒ M < 100,000,000

⇒ M <
`1 * 10^8` ...... (2)

Comparing (1) and (2) we can see that M can have more than 7 zeroes after 1 but LESS than 8 zeroes after 1.

So, the possible values of M can be:

`M = a * 10^7` where 1 < a ≤ 9

So, the EXPONENT USED BY PETER is 7 in all the possible cases.