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PSAT Math : Decimal Operations

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Example Questions

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Example Question #1 : How To Divide Decimals

Which number has 2.8 as its reciprocal?

Possible Answers:

$\frac{5}{1 4}$

$-\frac{5}{1 4}$

-8.2

-2.8

8.2

Correct answer:

$\frac{5}{1 4}$

Explanation:

The number that has 2.8 as its reciprocal is, in return, the reciprocal of 2.8.

$2.8 = \frac{28}{10} = \frac{28 \div 2}{10 \div 2} = \frac{14}{5}$

The reciprocal of this can be found by switching the numerator and the denominator. This is $\frac{5}{1 4}$ .

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Example Question #2 : How To Divide Decimals

23 grams of sodium are equal to $6.022 \times 10^{23}$ atoms. How many atoms comprise one milligram of sodium?

(Select the closest answer)

Possible Answers:

$1.39 \times 10 ^{20}$

$2.62 \times 10^{18}$

$2.62 \times 10^{17}$

$2.62 \times 10^{19}$

$1.39 \times 10 ^{19}$

Correct answer:

$2.62 \times 10^{19}$

Explanation:

23 grams are equal to 23,000 milligrams, so to find the number of atoms in one milligram, divide:

$=\frac{ 6.022 \times 10^{23} }{ 23,000}$

$=\frac{ 6.022 \times 10^{23} }{ 2.3 \times 10 ^{4} }$

$= \frac{ 6.022 }{ 2.3 } \cdot \frac{ 10^{23} }{ 10 ^{4} }$

$=2.62 \times 10^{19}$

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Example Question #21 : Decimals

Round the answer to the nearest tenth.

0.57-2.657=

Possible Answers:

2.0

-2.1

-2.0

-2.11

-2.05

Correct answer:

-2.1

Explanation:

0.57 - 2.657 = -2.087

Don't forget the negative sign!

This number then rounds to -2.1.

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Example Question #11 : Decimal Operations

Simplify:

-0.5+1.2-(0.6+0.1)

Possible Answers:

-2.4

0.2

-0.2

Correct answer:

Explanation:

Start by simplifying within the parentheses:

-0.5+1.2-(0.6+0.1)

-0.5+1.2-(0.7)

Then add/subtract each number

0.7-0.7 = 0

When you finish simplifying, the answer is 0.

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Example Question #1 : How To Subtract Decimals

Find the difference.

330.134 - 13.1

Possible Answers:

317.034

317.133

206.056

299.134

Correct answer:

317.034

Explanation:

(330-13) + (.134-.1) = 317+.034 = 317.034

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Example Question #1 : How To Convert Decimals To Scientific Notation

Convert 0.0004640 into scientific notation.

Possible Answers:

$4.64 \times 10^4$

$4.64\times10^{-4}$

The value is already in scientific notation

4640

$4640\times10^{-4}$

Correct answer:

$4.64\times10^{-4}$

Explanation:

When written in scientific notation, a number will follow the format x*10^y in which is between one and ten and is an integer value.

To find , take the first non-zero digit in your given number as the ones place. In 0.0004640 this would be the first 4. All subsequent digits fall into the tenths, hundredths, etc. places.

x=4.640

To find , we must count the number of places that is removed. In 0.0004640, the first digit of is in the ten-thousandths place. This indicates that will be .

Together, the final scientific notation will be $4.640*10^{-4}$ .

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Example Question #1 : How To Convert Decimals To Scientific Notation

Express 770,000,000,000 in scientific notation.

Possible Answers:

$0.77 \times 10^{12}$

$77 \times 10^{10}$

$7.7 \times 10^{11}$

$77 \times 10^{11}$

$7.7 \times 10^{10}$

Correct answer:

$7.7 \times 10^{11}$

Explanation:

Write the number with a decimal point and without commas:

$770 \; 000 \; 000 \; 000.$

Counting the number of places, move the decimal point to the left until it is after the first nonzero digit:

$7.70 \; 000 \; 000 \; 000$

The resulting number is 7.7; the number of places the decimal point moved to the left was 11. In scientific notation, this number is $7.7 \times 10^{11}$ .

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Example Question #1 : How To Convert Decimals To Scientific Notation

Convert 1362000 into scientific notation.

Possible Answers:

1.362*10^7

13.62*10^5

1.362*10^6

13.62*10^6

1.362*10^5

Correct answer:

1.362*10^6

Explanation:

To convert a number into scientific notation, the decimal must be moved until our base number is greater than 1 and less than 10. Next, we must count the number of places we moved it and multiply it by 10 to that number. Thus, our answer is:

1.362*10^6

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Example Question #4 : How To Convert Decimals To Scientific Notation

12 grams of oxygen are equal to $6.022 \times 10^{23}$ atoms. Which of the following comes closest to the mass, in grams, of one million atoms of oxygen?

Possible Answers:

$7.22 \times 10 ^{-28}$

$1.99 \times 10 ^{-29}$

$1.99 \times 10 ^{-17}$

$5.03 \times 10 ^{-18}$

$7.22 \times 10 ^{-16}$

Correct answer:

$1.99 \times 10 ^{-17}$

Explanation:

In scientific notation, one million atoms is equal to $1 \times 10^{6}$ atoms. To find the mass of this many atoms, we can solve the proportion statement

$\frac{m}{1 \times 10^{6}} = \frac{12} {6.022 \times 10^{23}}$

$m= \frac{12} {6.022 \cdot 10^{23}} \cdot \left (1 \times 10^{6} \right )$

$m= \frac{12 \cdot 10^{6}} {6.022 \cdot 10^{23}}$

$m= \frac{12} {6.022} \cdot \frac{10^{6}}{10^{23}} \approx 1.99 \times 10 ^{-17}$

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Example Question #1 : How To Convert Decimals To Scientific Notation

Define an operation $\bigstar$ as follows:

For all real numbers a,b ,

$a\bigstar b=a - b + 0.00000001$

Which of the following is equal to $0.00005 \bigstar 0.0000006$ ?

Possible Answers:

$4.941 \times 10 ^{-5}$

$4.941 \times 10 ^{-4}$

$4.401 \times 10 ^{-4}$

$4.401 \times 10 ^{-5}$

$4.939 \times 10 ^{-5}$

Correct answer:

$4.941 \times 10 ^{-5}$

Explanation:

Substitute and execute the operations:

$a\bigstar b=a - b + 0.00000001$

$0.00005 \bigstar 0.0000006 = 0.00005 - 0.0000006 + 0.00000001$

= 0.0000494 + 0.00000001

=0.00004941

Move the decimal point right five places to get it after the first nonzero digit; the scientific notation equivalent is

$4.941 \times 10 ^{-5}$

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PSAT Math : Decimal Operations

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : How To Divide Decimals

Example Question #2 : How To Divide Decimals

Example Question #21 : Decimals

Example Question #11 : Decimal Operations

Example Question #1 : How To Subtract Decimals

Example Question #1 : How To Convert Decimals To Scientific Notation

Example Question #1 : How To Convert Decimals To Scientific Notation

Example Question #1 : How To Convert Decimals To Scientific Notation

Example Question #4 : How To Convert Decimals To Scientific Notation

Example Question #1 : How To Convert Decimals To Scientific Notation

All PSAT Math Resources

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