To convert the decimal into a fraction, we can set up a proportion such that some number out of 100 is equal to the decimal.

Multiply by 100 on both sides.

The fraction we will need to reduce is:

To eliminate the decimal we can move the decimal place to the right one place on the top and bottom.

The answer is:  

Multiply the number of cups of sugar per batch, , by the number of batches Brenda wants to make, 8.

Rewrite both numbers as improper fractions as follows:

Multiply the fractions by multiplying numerators, then denominators:

Rewrite as a mixed number by dividing the numerator by the denominator:

, so 

Brenda needs more than the ten cups of sugar she has on hand.

Perform the same steps with flour. Since Brenda needs  cups per batch:

, so 

Brenda needs 10 cups of flour, the exact amount she has on hand. 

Brenda has enough flour but not enough sugar.

Add the decimal expressions as you would integers: append placeholder zeroes so that each number has the same number of decimal places, line up decimal points; add, (temporarily) disregarding the decimal points, and, in the sum, line up the decimal point with those in the addends. The result:

Multiply by 6 as you would integers, again (temporarily) disregarding the decimal point; place the decimal point in the product so that three digits are to the right (the total number in the factors):

Round this to the nearest whole number by noting that the next digit to the right (the tenths digit) is 3; therefore, round down to 82, the correct response.

The sum of the numbers of miles Peter ran is

Rewrite the expressions in terms of halves, and add numerators:

This is the correct response.

Simplify the following expression:

To begin, let's recall that dividing by a fraction is the same thing s multiplying by its reciprocal.

Therefore our original expression becomes:

Now, we should also recall that when multiplying fractions, we simply multiply across the top and the bottom to get our answer. This means we can combine these three fractions into one big fraction.

Now, we could just go to our calculator and plug this in and multiply it all out, but first let's simplify by removing common factors on the top and bottom.

Now, cancel out those factors found in both 

Those pairs of numbers will cancel to yield:

Scientific notation is written in the form .

In this equation, to go from standard to scientific notation, the decimal is shifted four places to the left.

When calculating standard notation from scientific notation, if the exponent is negative, the decimal point must move that number of spaces to the left. If the exponent is positive, the decimal point must move that number of spaces to the right. In this problem, the exponent is negative, therefore we must move the decimal three places to the left:

A number that is wrtiten in scientific notation includes the number with a decimal point after the first number and  , where is the number of times you need to move the decimal point.

So, if you write in scientific notation, it would be: , which is equivalent to . This shows that you need to move the decimal point two places to the right so it equals . Similarly, would be , which is equivalent , where you move the decimal point three places to the left.

becomes , which is equivalent . You would move the decimal point five places to the right to go back to .

A number that is wrtiten in scientific notation includes the number with a decimal point after the first number and  , where is the number of times you need to move the decimal point.

So, if you write in scientific notation, it would be: , which is equivalent to . This shows that you need to move the decimal point two places to the right so it equals . Similarly, would be , which is equivalent , where you move the decimal point three places to the left.

 becomes , which is equivalent . You would move the decimal point three places to the left to go back to .

Apply the exponent properties:

or, more correctly, .