Question

analysis of data
answer in complete sentences – no sentence = no credit

1. between standard and scientific notation, which form takes the most space to write?

standard notation takes the most space to write.

1. between standard and scientific notation, which form takes the most time to write?

standard notation takes the most time to write.

1. name one more problem encountered with writing the numbers in standard notation.

1. why do the last two numbers have negative exponents when written in scientific notation?

1. is the exponent for a number in scientific notation equal to the number of zeroes the number has in standard notation?

1. the numbers in this lab are all appropriate uses of scientific notation. can you think of a number (not necessarily listed above) that it would be inappropriate to use scientific notation for? if so, why is that number inappropriate? if not, why should all numbers be written in scientific notation?

Explanation:

Question 3

A problem with standard notation is that for very large or small numbers, it's easy to miscount digits, leading to errors. For example, writing \( 1000000000 \) (10 zeros) can have a digit missed, altering the value.

Numbers with negative exponents in scientific notation are very small (less than 1 in absolute value). The negative exponent indicates we move the decimal point to the left, showing the number is a fraction or decimal less than 1. For example, \( 5\times10^{-3}=0.005 \), as the exponent -3 means dividing by \( 10^3 \).

The exponent in scientific notation isn't always the number of zeros. For example, \( 2.5\times10^3 = 2500 \) (2 zeros, exponent 3) or \( 5\times10^{-2}=0.05 \) (1 zero, exponent -2). The exponent relates to the number of places the decimal moves, not just zeros.

Answer:

A problem with writing numbers in standard notation is that it is easy to miscount the number of digits (especially for very large or very small numbers), which can lead to errors in representing the number.

Question 4