Question

The doctor needs to determine whether the lab result is higher than 10 billion cells per liter. Enter the values in the boxes in scientific notation to compare.

Express 10 billion in scientific notation:

a) 1×10^9
b) 10×10^8
c) 1×10^10
d) 100×10^7

Express the lab result in scientific notation:

a) 2×10^9
b) 1.5×10^10
c) 8×10^9
d) 1.2×10^10

Answer 1

The correct expression of 10 billion in scientific notation is 1×1010. A lab result of 1.5×1010 is higher than 10 billion cells per liter, where 2×109 would be lower than that threshold.

Step-by-step explanation:

To express 10 billion in scientific notation, we must write the number so that it falls between 1 and 10 followed by an exponent representing the number of places the decimal point was shifted. 10 billion is 10,000,000,000 which can be written as 1 followed by 10 zeros, or 1×1010. Therefore, the correct expression in scientific notation is 1×1010, which corresponds to the option c) 1×1010.

Regarding the lab result, scientific notation should also follow the same rule and must have only one non-zero digit to the left of the decimal point. For example, if the lab result is 1.5×1010, it is already in proper scientific notation and directly comparable to 10 billion, which we established as 1×1010. Hence, if the lab result is option b) 1.5×1010, it indeed is higher than 10 billion cells per liter. In contrast, a lab result of 2×109 (option a) is less than 10 billion cells per liter.