What is the 2007th digit to the right of the decimal point in the decimal expansion of 1/7?

decimal expansion of 1/7 is 0.14285714285

Notice the 6th digit is 7, the 7th digit is 1, the 8th digit is 4, etc…

Therefore, you just divide which digit you want to know by 6, then look at the digit of the remainder. If the remainder is 0, then you are looking at the 6th digit.

For example if you want to know the 13th digit, 13/6 = 2 remainder 1. Therefore, you look at the first digit.

so for 2007 th digit we have,

2007/6= 334 , remainder 3, so we look at third digit , which is 2

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.

d. 145*2 is 290 than the total angle is 360 then minus 290 then divide by two