Question

8. Write `6.43\cdot10^{3}` in standard notation

9. Write `8.456\cdot10^{7}`

10. Write `8\cdot10^{5}` in standard notation

11. Write `9\cdot10^{10}` in standard notation

12. Describe how you would write 3,482,000,000 in scientific notation as if you were explaining it to someone who didn't know what scientific notation was.

Answer 1

just move the decimal point where the exponent indicates

there are no negative exponents here so none of these numbers will be decimal:

8. 6430, moved the decimal point 3 places to the right

9. 84560000 moved the decimal point 7 places to the right

10. 800000 (six zeros)

11. 90000000000 (ten zeros)

12. 3.482^9 (I'll use this one as example)

To convert a number to scientific notation, move the point just after the first number from left to right (that is not zero), remove the zeros that are from right to left if there are any (for example, if you have 45002 it is not needed to remove any because there is a significant number is in front of the two zeros, instead, if we have a number like 2046000, the last three zeros are removed).

there you will have the number: 3.482

Then, count how many places the point moved (in the original number) and that will be the exponent

3,482,000,000

moved 9 places

this isn't a decimal number so the exponent will be positive

3.482^9