Scientific Notation Jeopardy

Converting Standard Form to Scientific Notation

100

What is 64,830,000 in scientific notation? A) 64.83 x 10^6 B) 6.483 x 10^8 C) 6.483 x 10^9 D) 6.483 x 10^7

The answer is D) 6.483 x 10^7. To solve this, you have to move the decimal point until the number is in between 1 and 10. In 64,830,000 you move the decimal point seven spaces to the left, forming the number 6.4830000. 6.483 is multiplied by 10^7 because you had to move the decimal point seven spaces to the left to get 6.483. The exponent is not "-7" because the number 64,830,000 is greater than 1.

200

What is 47 billion in scientific notation?

The answer is 4.7 x 10^10. To solve this, first you have to find out what "47 billion" is in standard form (47,000,000,000). Next, you have to move the decimal point until the number is in between 1 and 10. In 47,000,000,000 you move the decimal point ten spaces to the left, forming the number 4.7000000000. 4.7 is multiplied by 10^10 because you had to move the decimal point ten spaces to the left to get 4.7. The exponent is not "-10" because the number 47,000,000,000 is greater than 1.

300

What is 0.000006923 in scientific notation?

The answer is 6.923 x 10^-6. To solve this, you have to move the decimal point until the number is in between 1 and 10. In 0.000006923 you move the decimal point six spaces to the right, forming the number 6.923. 6.923 is multiplied by 10^-6 because you had to move the decimal point six spaces to the right to get 6.483. The exponent is not "6" because the number 0.000006923 is less than 1.

400

What is 1,046,085,948,000 in scientific notation?

The answer is 1.046085948 x 10^12. To solve this, you have to move the decimal point until the number is in between 1 and 10. In 1,046,085,948,000 you move the decimal point twelve spaces to the left, forming the number 1.046085948000. 1.046085948 is multiplied by 10^12 because you had to move the decimal point twelve spaces to the left to get 1.046085948. The exponent is not "-12" because the number 1,046,085,948,000 is greater than 1.

500

What is twenty-eight thousand, three hundred seventy-four ten-trillionths in scientific notation?

The answer is 2.8374 x 10^-9. To solve this, first you have to find out what "twenty-eight thousand, three hundred seventy-four ten-trillionths" is in standard form (0.0000000028374). Next, you have to move the decimal point until the number is in between 1 and 10. In 0.0000000028374 you move the decimal point nine spaces to the right, forming the number 2.8374. 2.8374 is multiplied by 10^-9 because you had to move the decimal point nine spaces to the right to get 2.8374. The exponent is not "9" because the number 0.0000000028374 is less than 1.

Converting Scientific Notation to Standard Form

100

What is 3.564 x 10^5 in standard form? A) 35,640,000 B) 356,400 C) 3,564,000 D) 35,640

The answer is B) 356,400. To solve this, you have to move the decimal point in the direction and number of places the exponent tells you to (For positive exponents, move to the right. For negative exponents, move to the left. The number of places moved is the absolute value of the exponent). In 3.564 you move the decimal point five spaces to the right because 3.564 is being multiplied by 10^5. This forms the number 356,400.

200

What is five and two tenths times ten to the sixth power in standard form?

The answer is 5,200,000. To solve this, first you have to find out what "five and two tenths times ten to the sixth power" is in standard form (5.4 x 10^6). Next, you have to move the decimal point in the direction and number of places the exponent tells you to (For positive exponents, move to the right. For negative exponents, move to the left. The number of places moved is the absolute value of the exponent). In 5.2 you move the decimal point six spaces to the right because 5.2 is being multiplied by 10^6. This forms the number 5,200,000.

300

What is 3.078 x 10^-5 in standard form?

The answer is 0.00003078. To solve this, you have to move the decimal point in the direction and number of places the exponent tells you to (For positive exponents, move to the right. For negative exponents, move to the left. The number of places moved is the absolute value of the exponent). In 3.078 you move the decimal point five spaces to the left because 5.2 is being multiplied by 10^-5. This forms the number 0.00003078.

400

What is 6.000004217 x 10^9 in standard form?

The answer is 6,000,004,217. To solve this, you have to move the decimal point in the direction and number of places the exponent tells you to (For positive exponents, move to the right. For negative exponents, move to the left. The number of places moved is the absolute value of the exponent). In 6.000004217 you move the decimal point nine spaces to the right because 6.000004217 is being multiplied by 10^9. This forms the number 6,000,004,217.

500

What is six and twenty-seven million, three hundred eighty-four thousand, nine hundred five ten millionths x 10^-7?

The answer is 0.000000627384905. To solve this, first you have to find out what "six and twenty-seven million, three hundred eighty-four thousand, nine hundred five ten millionths x 10^-7" is in standard form (6.27384905 x 10^-7). Next, you have to move the decimal point in the direction and number of places the exponent tells you to (For positive exponents, move to the right. For negative exponents, move to the left. The number of places moved is the absolute value of the exponent). In 6.27384905 you move the decimal point seven spaces to the left because 6.27384905 is being multiplied by 10^-7. This forms the number 0.000000627384905.

Word Problems

100

Light travels about 1.8 x 10^7 kilometers in a minute. What is 1.8 x 10^7 km in standard form?

The answer is 18,000,000 km. To solve this, you have to move the decimal point in the direction and number of places the exponent tells you to (For positive exponents, move to the right. For negative exponents, move to the left. The number of places moved is the absolute value of the exponent). In 1.8 you move the decimal point seven spaces to the right because 1.8 is being multiplied by 10^7. This forms the number 18,000,000.

200

Bill Gates has 5.6 x 10^10 dollars. How much is that is standard form?

The answer is $56,000,000,000. To solve this, you have to move the decimal point in the direction and number of places the exponent tells you to (For positive exponents, move to the right. For negative exponents, move to the left. The number of places moved is the absolute value of the exponent). In 5.6 you move the decimal point ten spaces to the right because 5.6 is being multiplied by 10^10. This forms the number 56,000,000,000.

300

A picometer is one trillionth of a meter. The diameter of a helium atom is 62 picometers. How many meters is the diameter of a helium atom? Express your answer in scientific notation.

The answer is 6.2 x 10^-11 meters. To solve this, first you have to find out what 62 picometers is in meters. You do this by multiplying 62 by 0.000000000001. 62 x 0.000000000001 = 0.000000000062. Next, you have to find out what 0.000000000062 is in scientific notation. To do this, you have to move the decimal point until the number is in between 1 and 10. In 0.000000000062 you move the decimal point eleven spaces to the left, forming the number 6.2. 6.2 is multiplied by 10^-11 because you had to move the decimal point eleven spaces to the right to get 6.2. The exponent is not "11" because the number 0.000000000062 is less than 1. So, the diameter of a helium atom is 6.2 x 10^-11 meters.

400

The sun weighs around 1,989,000,000,000,000,000,000,000,000,000 kilograms. How many grams does the sun weigh? One kilogram is equal to one thousand grams. Express your answer in scientific notation.

The answer is 1.989 x 10^33 grams. To solve this, first you have to multiply the sun's weight in kilograms by 1,000 to find out how many grams the sun weighs. 1,989,000,000,000,000,000,000,000,000,000 x 1,000 = 1,989,000,000,000,000,000,000,000,000,000,000 So the sun weighs 1,989,000,000,000,000,000,000,000,000,000,000 grams. Next, you have to move the decimal point until the number is in between 1 and 10. In 1,989,000,000,000,000,000,000,000,000,000,000 you move the decimal point thirty-three spaces to the left, forming the number 1.989000000000000000000000000000000. 1.989 is multiplied by 10^33 because you had to move the decimal point thirty-three spaces to the left to get 1.989. The exponent is not "-33" because the number 1,989,000,000,000,000,000,000,000,000,000,000 is greater than 1. So the sun weighs 1.989 x 10^33 grams.

500

The Milky Way Galaxy is approximately 1 x 10^5 light years in diameter. A light year is how far light travels in one year. Assuming that light travels 9.4608 x 10^10 kilometers in a year, how many meters long is the Milky Way Galaxy's diameter? Express your answer in standard form.

The answer is 9,460,800,000,000,000,000 meters. To solve this, first you have multiply 1 x 10^5 by 9.4608 x 10^10 (100,000 x 94,608,000,000 = 9,460,800,000,000,000). You do this to find out what the Milky Way Galaxy's diameter is in kilometers. So the diameter of the Milky Way Galaxy is 9,460,800,000,000,000. Next, you multiply 9,460,800,000,000,000 by 1,000 to find out how many meters the Milky Way Galaxy's diameter is (9,460,800,000,000,000 x 1,000 =9,460,800,000,000,000,000). So the diameter of the Milky Way Galaxy is 9,460,800,000,000,000,000 meters.

Miscellaneous

100

What is scientific notation a shortcut for?

Scientific notation is a shortcut for writing very large or very small numbers.

200

What is the following procedure used for? Move the decimal point in the direction and number of places the exponent tells you (For positive exponents, move to the right. For negative exponents, move to the left. The number of places moved is the absolute value of the exponent).

To convert numbers between Scientific Notation to Standard Form

300

What are the following steps used for? 1) Move the decimal point until the number is in between 1 and less than 10. 2) Find the sign of the exponent (Positive for numbers>1 and Negative for numbers<1). 3) Count the places moved for the exponent.

To convert numbers between Standard Form to Scientific Notation

400

How is a number in scientific notation written?

A number in scientific notation is written as the product of two factors. The first factor is a number that has an absolute value greater than or equal to 1 and less than 10. The second factor is a power of 10.

500

Give four examples of objects that should be measured in scientific notation (Two positive exponent examples and two negative exponent examples).

Possible Positive Exponent Examples: -The mass of the Earth -The number of people in the world -The distance light travels in a year -The number of stars in the Milky Way Galaxy -The distance from the Earth to the Sun Possible Negative Exponent Examples: -The diameter of an atom -The mass of a cell -The diameter of a nucleus -The size of a grain of sand -The size of a grain of salt