Solved on Sep 07, 2023

Convert measurements to scientific notation: a. 1.2×109dL1.2 \times 10^9 \mathrm{dL} b. 6.7×1011mm6.7 \times 10^{-11} \mathrm{mm} c. 6.7×1010g6.7 \times 10^{10} \mathrm{g}

STEP 1

Assumptions1. We are asked to write the given numbers in exponential notation. . Exponential notation is a way of writing a number that is too large or too small to be conveniently written in decimal form. It is written as a product of a number between1 and10 and a power of10.

STEP 2

Let's start with the first part (a). The number is 1200000000d1200000000 \mathrm{d}.
We can write this number in exponential notation by identifying the number of places the decimal point needs to move to be between the first and second non-zero digits.

STEP 3

Move the decimal point9 places to the left to get 1.21.2. The number of places moved is the exponent of10.
So, 1200000000d1200000000 \mathrm{d} can be written as 1.2×109d1.2 \times10^9 \mathrm{d}.

STEP 4

Next, let's move on to part (b). The number is 0.000000000067mm0.000000000067 \mathrm{mm}.
Again, we will move the decimal point, but this time to the right until it is between the first and second non-zero digits.

STEP 5

Move the decimal point11 places to the right to get .7.7. The number of places moved is the negative of the exponent of10.
So, 0.000000000067mm0.000000000067 \mathrm{mm} can be written as .7×1011mm.7 \times10^{-11} \mathrm{mm}.

STEP 6

Finally, let's solve part (c). The number is 67000000000g67000000000 \mathrm{g}.
As before, we will move the decimal point to the left until it is between the first and second non-zero digits.

STEP 7

Move the decimal point10 places to the left to get 6.76.7. The number of places moved is the exponent of10.
So, 67000000000g67000000000 \mathrm{g} can be written as 6.7×1010g6.7 \times10^{10} \mathrm{g}.
The solutions to the problem area. 1200000000d=1.2×109d1200000000 \mathrm{d} =1.2 \times10^9 \mathrm{d} b. 0.000000000067mm=6.7×1011mm0.000000000067 \mathrm{mm} =6.7 \times10^{-11} \mathrm{mm} c. 67000000000g=6.7×1010g67000000000 \mathrm{g} =6.7 \times10^{10} \mathrm{g}.

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