N21 | Maths Made Easy

N21

QUESTION:

i) Write 300,950,000 in standard form.

ii) Write 1.997\times{10}^{-7} in decimal notation.

 

ANSWER:

i) We need to see how many times we must move the decimal point to make the number fall between 1 and 10. If we move it 8 times, ,then it becomes 3.0095, which falls between 1 and 10. This is a big number, so its power is positive, and we get

300,950,000 = 3.0095\times10^8

ii) This is a negative power so want to end up with a small number – we must divide by 10 seven times. So, moving the decimal place 7 spaces to the left, we get

1.997\times10^{-7}=0.0000001997