SAT Math : Decimals

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #401 : Arithmetic

Which of the following represents the quotient

in scientific notation?

Possible Answers:

Correct answer:

Explanation:

A number in scientific notation takes the form , where  and is an integer.

Split the fraction as follows:

Apply the Quotient of Powers Rule:

However,  is not in scientific notation, since .

Adjust by noting that ; substitute and apply the Product of Powers Rule:

Example Question #21 : How To Convert Decimals To Scientific Notation

Which of the following represents the quotient

in scientific notation?

Possible Answers:

Correct answer:

Explanation:

A number in scientific notation takes the form , where  and is an integer.

Split the quotient as follows:

Applying the Quotient of Powers Rule:

However,   is not in scientific notation, since . Adjust by noting that ; substituting and applying the Product of Powers Rule:

Example Question #402 : Arithmetic

Which of the following represents the cube of  in scientific notation?

Possible Answers:

None of the other choices gives the correct response.

Correct answer:

Explanation:

A number in scientific notation takes the form , where  and is an integer.

To find , apply the Power of a Product Rule, then the Product of Powers Rule, as follows:

However, since , this number is not in scientific notation. Adjust by noting that , then applying the Product of Powers Rule again:

,

the correct response.

Example Question #401 : Arithmetic

Round 901,527 to the nearest thousand and convert to scientific notation. 

Possible Answers:

Correct answer:

Explanation:

When rounding to the nearest thousand, look to the hundreds place to determine whether you need to round up or down. You always round down when the digit is between 0 and 4, and up when it is between 5-9. Therefore, the rounded number is 902,000. When using scientific notation, the first number in the notation must be less than 10. In this case, that number is 9.

From there, the decimal goes immediately after. Then count how many places the decimal would have to be moved in order to convert back to the original number (5 places).

 

When the decimal is moved to the left when writing it in scientific notation, the exponent is positive. When moved to the right to write the number in scientific notation, the exponent is negative. 

Example Question #21 : How To Convert Decimals To Scientific Notation

Express the result in scientific notation:

Possible Answers:

Correct answer:

Explanation:

First, rewrite 200,000,000 as a number in scientific notation. A number in scientific notation takes the form , where  and is an integer.

200,000,000 can be rewritten by adding the implied decimal point to the end of the number, and move it to the left until it follows the first nonzero digit - the "2" - as seen below:

Scientific

Since the decimal point was moved 8 places to the left to form the number 2, the number, expressed in scientific notation, is .

Therefore, . By the Negative Exponent Rule , 

, so

Applying the Power of a Product Property, we get

Applying the Negative Exponent Rule and the Power of a Product Property on the right, we get

Therefore, .

Applying the Power of a Product Property:

Applying the Product of Powers Property:

Since , this is not in scientific notation; adjust it by noting that

substituting, and applying the Product of Powers Property:

Example Question #66 : Decimals

Express the following number in scientific notation:

Possible Answers:

Correct answer:

Explanation:

A number in scientific notation takes the form , where  and is an integer.

To convert 3,880,000,000,000 to scientific notation, place the implied decimal point after the final zero and move it to the left as many places as is necessary until it is after the first nonzero digit - in this case the "3". Note that the point is moved 12 places to the left.

Scientific

The number in front is 3.88, the number formed. The exponent of 10 is 12 - positive since the point was moved to the left. Therefore, the number, in scientific notation, is .

Example Question #21 : How To Convert Decimals To Scientific Notation

Express the result in scientific notation:

Possible Answers:

None of these

Correct answer:

None of these

Explanation:

A number in scientific notation takes the form , where  and is an integer.  

An easy way to add these numbers is to note that if  and  are both positive integers,  is the number  followed by  zeroes. Therefore, 

Add these numbers:

Since all four choices can be rewritten as 6 followed by a number of zeroes, none of them are equal to this sum. 

Example Question #22 : How To Convert Decimals To Scientific Notation

Which of the following represents the product of

in scientific notation?

Possible Answers:

None of these

Correct answer:

Explanation:

A number in scientific notation takes the form , where  and is an integer.

To multiply two numbers that are in scientific notation, first, use commutativity to multiply the numbers:

Applying the Product of Powers Rule on the powers of 10:

However, since , this number is not in scientific notation. Adjust by noting that , then applying the Product of Powers Rule again:

Example Question #1 : How To Add Decimals

If Johnny buys two comic books, priced at $1.50 each, and a candy bar, priced at $0.75, he'll have three quarters and two dimes left over.  How much money does he have right now?

Possible Answers:

$5.10

$4.70

$3.75

$4.35

$3.20

Correct answer:

$4.70

Explanation:

Add what he can purchase to what he has left over:

Two comic books and the candy bar: $1.50 + $1.0 + $0.75 = $3.75

Three quarters and two dimes: $0.75 + $0.20 = $0.95

Therefore his total amount of money is $3.75 + $0.95 = $4.70.

Example Question #411 : Arithmetic

Add:  

Possible Answers:

Correct answer:

Explanation:

In order to add the decimals, add placeholders to the decimal .

Be careful not to add the wrong digits!

Add the thousandths places.

Add the hundredths places.

Add the tenths places.

Combine the numbers and put a decimal before the tenths place.

The correct answer is:  

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