Multiplying and Dividing in Scientific Notation 7 th Grade Math

World War II On August 2, 1939, just before the beginning of World War II, Albert Einstein wrote a letter to President Franklin D. Roosevelt. Einstein and several other scientists told Roosevelt of efforts in Nazi Germany to purify uranium which could be used to build an atomic bomb. It was shortly thereafter, that the United States Government began a serious undertaking known as the “Manhattan Project.” Simply put, the Manhattan Project was committed to building the first atomic bomb.

World War II Over the course of six years, from 1939 – 1945, more than $2 billion was spent during the history of the Manhattan Project! At 5:25 on July 16, 1945 the first atomic bomb was tested at the White Sands Missile Range in New Mexico. On Monday, August 6, 1945, the nuclear bomb nicknamed “Little Boy” was dropped on Hiroshima, Japan. On August 9, 1945, Nagasaki was the target of the world’s second atomic bomb attack. That bomb was nicknamed “Fat Man.” On August 10, 1945, Japan surrendered.

What does WWII have to do with scientific notation? Mass of a Hydrogen atom: Proton (positive charge): = 1.67 x Electron (negative charge): = x

Speed of Sound US Navy Jet (FA-18) broke the sound barrier on July 7, The white halo is formed by condensed water droplets which are thought to result from a drop in air pressure around the aircraft. Speed of Sound: 1,126 ft. per sec. = x 10 3 ft. per sec.

Great Wall of China 29,040,000 feet long = x 10 7 feet long

Circumference of the Earth 24,901 miles x 10 4 miles

Multiplying in Scientific Notation Multiply the decimal numbers. Multiply the decimal numbers. Then add the exponents of the powers of 10. Then add the exponents of the powers of 10. Place the new power of 10 with the decimal in scientific notation form. Place the new power of 10 with the decimal in scientific notation form. If your decimal number is greater than 10, count the number of times the decimal moves to the left, and add this number to the exponent. If your decimal number is greater than 10, count the number of times the decimal moves to the left, and add this number to the exponent.

Example: Multiply (2.6 x 10 7 ) by (6.3 x 10 4 ) Multiply the decimal numbers. Multiply the decimal numbers x 6.3 = Add the exponents. Add the exponents = Put the new decimal number with the new exponent in scientific notation form. Put the new decimal number with the new exponent in scientific notation form x 10 11

Example: Multiply (2.6 x 10 7 ) by (6.3 x 10 4 ) Because the new decimal number is greater than 10, count the number of places the decimal needs to move to put the number between 1 and 10. Add this number to the exponent. Because the new decimal number is greater than 10, count the number of places the decimal needs to move to put the number between 1 and 10. Add this number to the exponent. In this case, the decimal point moves one place, so add 1 to the exponent. In this case, the decimal point moves one place, so add 1 to the exponent x = x 10 12

You Try! Simplify the following: Simplify the following: a.(2.5 x 10 7 ) x (3 x 10 3 ) = b. (4.4 x 10 6 ) x (3.9 x 10 4 ) =

Dividing in Scientific Notation Divide the decimal numbers. Divide the decimal numbers. Then subtract the exponents of the powers of 10. Then subtract the exponents of the powers of 10. Place the new power of 10 with the decimal in scientific notation form. Place the new power of 10 with the decimal in scientific notation form. If your decimal number is less than 1, move the decimal point to the right and decrease the exponent by the number of places that the decimal point was moved. If your decimal number is less than 1, move the decimal point to the right and decrease the exponent by the number of places that the decimal point was moved.

Example: Divide (1.3 x ) ÷ (2.4 x 10 4 ) Divide the decimal numbers. Divide the decimal numbers ÷ 2.4 = Subtract the exponents. Subtract the exponents. 11 – 4 = Put the new decimal number with the new exponent in scientific notation form. Put the new decimal number with the new exponent in scientific notation form x 10 7

Example: Divide (1.3 x ) ÷ (2.4 x 10 4 ) Because the decimal number is not between 1 and 10, move the decimal point one place to the right and decrease the exponent by 1. Because the decimal number is not between 1 and 10, move the decimal point one place to the right and decrease the exponent by 1. In this example, the decimal moves one place, so subtract 1 from the exponent. In this example, the decimal moves one place, so subtract 1 from the exponent x 10 7 = x 10 6

You Try! Simplify the following: Simplify the following: a.(5.76 x 10 9 ) ÷ (3.2 x 10 3 ) = b.(3 x 10 7 ) ÷ (8 x 10 4 ) =