In Exercises 31–50, perform the indicated computations. Write the...

Question

In Exercises 31–50, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places.0.00072x0.003 / 0.00024

Accepted Answer

Welcome back. I am so glad you're here. We are asked to evaluate the following set of operations and then express the result in scientific notation with two decimal places. If applicable, the operations were given our 0. times 0.6, divided by 0.24. Our answer choices are answer choice. A 3.2 times 10 to the negative to be 3.2 times 10 to the negative three C 2.3 times 10 to the -2 and D 2.3 times 10 to the -3. Alright. The first step in evaluating the set of operations, we've got all these decimal points here. We are going to turn each of these into scientific notation expressions. And we recall from previous lessons that scientific notation will have one digit to the left of the decimal point. That one digit will be between one and nine, all three of these are zero to the left of the decimal point. So we're going to need to move that decimal point then to the right of the decimal point. We have all of the rest of the non zero numbers until we hit only zeros. And then the whole thing will be times 10 raised to an exponent. Right. Now, all three of these are actually times 10 raised to the exponents zero because we recall from previous lessons that 10 raised to the zero. That's just one. So we can multiply all of these by one and they remain themselves and that will be important in a moment. Okay. So now let's first work on getting that number one through nine to the left of the decimal. And in order to do that for all three of these, we need to move the decimal for the 1st 10.92. We're going to move the decimal to the right 1234 times. So we're moving to the right four units. When we move to the right, we are lowering The decimal of the times raised to the not decimal exponent, we are lowering the exponent of the times 10 raised to the exponent. So we're going to lower it by the amount of spaces that we move the decimal. So in this case for the first one, we've moved it to the right four. So we're going to subtract four from our times 10 to the zero from the zero. So we will have the digit to the left of the decimal is going to be nine and then our decimal point and then all of the rest of the non zero numbers. So to and then times 10 raised to the zero minus four, which is negative four. And we can bring down this times and now we can work on the next 10.6. That six is going to be our number to the left of our decimal point. So let's move it over 123 to the right, which means we are lowering our exponent by three or subtracting three from zero in 10 to the zero. So we will have 6.0 times raised to the zero minus three is negative three. Bring down the division symbol and this last one, we will have the to be the number to the left of our decimal point. So we'll move this over times to the right. So we'll be subtracting four from that zero in the exponent of times 10 raised to the zero. So we will have 2. times 10 raised to the zero minus four is still negative four. And now we've expressed all of these terms in scientific notation and now we can just do the multiplication and division for the parts that are alike. So let's start with the 9.2 times 6.0 divided by 2.4. So if we punch that into a calculator 9.2 times 6.0, divided by 2.4, that equals Now let's work on the second part here, this 10 to the negative fourth times 10 to the negative third, divided by 10 to the negative fourth. I'm going to rewrite that in a fraction. So the numerator has 10 to the negative fourth times 10 to the negative third and the denominator is 10 to the negative fourth. Now we recall from previous lessons that when we have like bases, those are the tens we are going to when multiplying the like bases, we are going to add the exponents. We're going to take negative four plus negative three in the numerator. And that will give us 10 raise to the negative four plus negative three is negative seven still being divided by 10 to the negative fourth. And now we recall that when we have like bases that are being divided, we are going to subtract their exponents. So we're going to take negative seven minus negative four, which is the same as negative seven plus four and negative seven plus four equals a negative three. So we have 10 raised to the negative three. So we can rewrite this in scientific notation. Well, not quite yet. First, we write 23 times 10 to the negative third. But why isn't that in scientific notation yet? Because we have two numbers to the left of the decimal point. There's an unwritten decimal point after the three and 23, we need to move it this time to the left one unit. And when we are moving to the left, we are raising our exponents by the number of digits that we're moving to the left. So because we're moving to the left one, we're going to add one to our exponent of negative three after the times 10. So now we'll have 2.3 times 10 raised to the negative three plus one is negative two. And there is our final answer In scientific notation, We look at our answer choices for 2.3 times 10 to the -2. And that matches with answer choice. C. Well done. We'll catch you on the next one.

In Exercises 31–50, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places.0.00072x0.003 / 0.00024

Key Concepts

Scientific Notation

Multiplication of Decimals

Division of Decimals

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