Question

small positive numbers in scientific notation

1. complete the table as directed during the lesson. the table shows an approximate measurement of various objects.

approximate measurement (meters)
standard form unit form fraction number times a unit fraction (expanded form) number times a unit fraction (exponential form)
grain of rice (length) 0.006 6 thousandths $\frac{6}{10^{3}}$ 6/1000 $6\times10^{-3}$
spider silk (diameter) 0.000004 4 millionths $\frac{4}{10^{6}}$ 4/1000000 $4\times10^{-6}$
water molecule (diameter) 0.0000000003 3 ten - billionths $\frac{3}{10^{10}}$ 3/10000000000 $3\times10^{-10}$
white blood cell (diameter) 0.000002 2 millionths $\frac{2}{10^{6}}$ 2/1000000 $2\times10^{-6}$

Explanation:

Step1: Recall scientific - notation rules

Scientific notation is of the form $a\times10^{n}$, where $1\leqslant|a|\lt10$ and $n$ is an integer.

Step2: Analyze the given numbers

For a number in standard form like $0.006$, we move the decimal point 3 places to the right to get $a = 6$ and since we moved the decimal point 3 places to the right, $n=- 3$, so it is $6\times10^{-3}$. For $0.000004$, we move the decimal point 6 places to the right to get $a = 4$ and $n=-6$, so it is $4\times10^{-6}$. For $0.0000000003$, we move the decimal point 10 places to the right to get $a = 3$ and $n=-10$, so it is $3\times10^{-10}$. For $0.000002$, we move the decimal point 6 places to the right to get $a = 2$ and $n=-6$, so it is $2\times10^{-6}$.

Answer:

The table is already filled correctly for the scientific - notation (exponential form) columns for each of the given measurements. The number in standard form is correctly converted to scientific notation (number times a unit fraction in exponential form) as follows:

• Grain of Rice: $6\times10^{-3}$
• Spider Silk: $4\times10^{-6}$
• Water Molecule: $3\times10^{-10}$
• White Blood Cell: $2\times10^{-6}$