Test: Scientific Notation - ACT MCQ

The equation factors to (x-4)(x+2)=0, indicating that the roots are x=-2,4. The sum of these two roots is 2.

350,000,000 = 3.5 x 10⁸ (exponent is equal to the number of decimal points shifted)

We plug in the value given for x and solve for y. 

2xy + 4x² - y = 2x

2(2)y + 4(2)² - y = 2(2)

4y + 4(4) - y = 4

4y - y + 16 = 4

3y = -12

y = -4

657800 = 6.578 × 10⁵

OR

657800 = 65.78 × 10⁴

Exponent on 10 is the number of decimal points over the number has shifted.

2 × 10⁰ + 3 × 10² + 4 × 10⁴ =

2 + 300 + 40,000 = 40,302

There are six zeros and two more number places, for a total of eight, so 125,000,000 is equivalent to 1.25 × 10⁸.

In this case the exponent is positive hence you have to move the decimal point 4 places to the right from where it is in the problem giving us 23,000

In this case you have to move the decimal point 6 places to the right. When you move the decimal point to the right the exponent becomes negative.  Similarly when you move the decimal point to the left the exponent is positive.  Also, to the left of the decimal place there can be only one digit.

3.4∗10⁻⁶

First, when we round to the nearest thousand we get 5, 679, 000 since we round up when the next digit is greater than 5.

Then, to put it in scientific notation, we arrange the digits so that a decimal point creates a number between 1 and 10. We get 5.679.

Then, we want the exponent of the 10 to be the number of times the decimal needs to move to the right. This is 6 times.

Thus, we get our answer.5.679 × 10⁶