Question

Allie Gaiter needs to study a star for her astronomy research project. She has narrowed her choices down to four stars and wants to study the one that is farthest from Earth. A-0.176*10^18 / B- 22.13*10^16 / C - 31.42*10^16 / D- 125.5*10^15

Answer 1

Answer: C

Explanation:

Convert each option into scientific notation (Only one digit between 1 and 9 before the decimal point). If you move the decimal place to the left, move the exponent that many units to the right. If you move the decimal place to the right, move the exponent that many units to the left.

`A)\quad 0.176* 10^(18)\quad =1.76* 10^(17)\\\text{moved the decimal 1 place to the right and the exponent 1 place to the left}\\\\B)\quad 22.13* 10^(16)\quad =2.213* 10^(17)\\\text{moved the decimal 1 place to the left and the exponent 1 place to the right}\\\\C)\quad 31.42* 10^(16)\quad =3.142* 10^(17)\\\text{moved the decimal 1 place to the left and the exponent 1 place to the right}`

`D)\quad 125.5* 10^(15)\quad =1.255* 10^(17)\\\text{moved the decimal 2 places to the left and the exponent 2 places to the right}`

Since they are all (× 10¹⁷), we can compare the digits:

1.76 2.213 3.142 1.255

The largest one is 3.142 so C is the answer.