To write in standard form, move the decimal point to the right until there is one non-zero digit to its left. The number of places moved becomes the negative exponent of 10.
The decimal point is moved 12 places to the right.
\[ 0.0000000000085 = 8.5 \times 10^{-12} \]
Move the decimal point 12 places to the right so that there is a single non-zero digit to the left of the decimal.
\[ 0.00000000000942 = 9.42 \times 10^{-12} \]
To write in standard form, move the decimal point to the left until there is one non-zero digit to its left. The number of places moved becomes the positive exponent of 10.
The decimal point is moved 15 places to the left.
\[ 6020000000000000 = 6.02 \times 10^{15} \]
Move the decimal point 9 places to the right.
\[ 0.00000000837 = 8.37 \times 10^{-9} \]
Move the decimal point 10 places to the left.
\[ 31860000000 = 3.186 \times 10^{10} \]
A negative exponent means the number is less than 1. Move the decimal point to the left by the number of places indicated by the exponent.
\[ 3.02 \times 10^{-6} = 0.00000302 \]
A positive exponent means the number is greater than 10. Move the decimal point to the right by the number of places indicated by the exponent.
\[ 4.5 \times 10^{4} = 45000 \]
Move the decimal point 8 places to the left.
\[ 3 \times 10^{-8} = 0.00000003 \]
Move the decimal point 9 places to the right.
\[ 1.0001 \times 10^{9} = 1000100000 \]
Move the decimal point 12 places to the right.
\[ 5.8 \times 10^{12} = 5800000000000 \]
Move the decimal point 6 places to the right.
\[ 3.61492 \times 10^{6} = 3614920 \]
\[ \frac{1}{1000000} \text{ m} = \frac{1}{10^6} \text{ m} = 1 \times 10^{-6} \text{ m} \]
Move the decimal point 19 places to the right.
\[ 0.00000000000000000016 \text{ C} = 1.6 \times 10^{-19} \text{ C} \]
Move the decimal point 7 places to the right.
\[ 0.0000005 \text{ m} = 5 \times 10^{-7} \text{ m} \]
Move the decimal point 5 places to the right.
\[ 0.00001275 \text{ m} = 1.275 \times 10^{-5} \text{ m} \]
Move the decimal point 2 places to the right.
\[ 0.07 \text{ mm} = 7 \times 10^{-2} \text{ mm} \]
First, find the total thickness of the books.
\[ \text{Thickness of 5 books} = 5 \times 20 \text{ mm} = 100 \text{ mm} \]
Next, find the total thickness of the paper sheets.
\[ \text{Thickness of 5 sheets} = 5 \times 0.016 \text{ mm} = 0.08 \text{ mm} \]
Add the two thicknesses to find the total thickness.
\[ \text{Total thickness} = 100 \text{ mm} + 0.08 \text{ mm} = 100.08 \text{ mm} \]
Express the answer in standard form as requested in the overall exercise.
\[ 100.08 \text{ mm} = 1.0008 \times 10^2 \text{ mm} \]
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