Question

Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the fraction bar(s).
A scientist measures the diameter of a bacteria cell and yeast cell. She finds the diameter of a bacteria cell to be 0.0000021 meters and the diameter of a yeast cell to be 0.00000398 meters.

The approximate diameter of the bacteria cell is represented by point ----------
on the number line.
The approximate diameter of the yeast cell is represented by point -----------
on the number line.
The diameter of the bacteria cell is approximately ----------
times smaller than the diameter of the yeast cell.

Answer 1

Since there are 5 zeros after the decimal point in front of the 21, 0.0000021=2.1*10^(-6) (by moving the decimal 6 places to the right, and we have 6 instead of 5 because we have to account for moving the 2 in front of the decimal too). For 0.00000398, we can use a similar process to get 3.98*10^(-6). Since 2.1 rounds to 2 (since 1<5) and 3.98 rounds to 4 (since 9>5), we have the approximate diameter of the bacteria cell be 2*10^(-6) and the yeast cell be *10^(-6)

Since we want to find how many times smaller the bacteria cell is,. we divide the bacteria cell by the yeast cell to get (2*10^(-6))/(4*10^(-6))=1/2=2/4, meaning that the bacteria cell is half as big as the yeast cell and the yeast cell is 2 times as big as the bacteria cell (since the reciprocal of 1/2 is 2)