GED Math Extra Prep: Scientific Notation

Practice Questions

1. What is the sum of
   

   (Note: You may not use a calculator.)

   

2. A human hair has an average diameter of
   

   What is the maximum number of human hairs that could fit side by side (without overlapping) on a microscope slide that is 50 millimeters wide? Write your answer in scientific notation.

   

Answers and Explanations

1. The correct answer is D.

   Rewrite the number with the smaller power of ten

   

   so that it has the same power of ten as the larger number:

   

   Now rewrite the sum using the newly converted number:

   

   Because the powers of ten for the two numbers are now the same, you can simply add the coefficients (the decimal parts) and keep the 10⁵ as it is:

   

   Hence, Choice (D) is the correct answer.

2. The correct answer is A.

   There are 1,000 millimeters in a meter, so convert the width of the microscope slide from millimeters into meters by dividing by 1,000 (or multiplying by 10^–3) to get

   

   Then, to find the number of hairs that can fit on the slide, you need to divide the width of the slide by the width of one hair.

   

   Many people make errors entering this on a calculator, so it's usually easier and quicker to perform this calculation by hand. Start by dividing 50 by 2.5 to get 20; then divide the powers of 10 by subtracting the bottom exponent from the top exponent:

   

   Now convert into scientific notation by rewriting 20 as

   

   (so the leading coefficient is between 1 and 9.9); then multiply the powers of 10 by adding the exponents:

   

   Hence, Choice (A) is correct.