Multiplying and Dividing in Scientific Notation

7th Grade Math

World War II

On August 2, 1939, just before the beginning ofWorld War II, Albert Einstein wrote a letter toPresident Franklin D. Roosevelt. Einstein andseveral other scientists told Roosevelt of effortsin Nazi Germany to purify uranium which couldbe used to build an atomic bomb. It was

shortlythereafter, that the United States Governmentbegan a serious undertaking known as the“Manhattan Project.” Simply put, theManhattan Project was committed to buildingthe first atomic bomb.

World War II

Over the course of six years, from 1939 – 1945,more than $2 billion was spent during the historyof the Manhattan Project! At 5:25 on July 16, 1945the first atomic bomb was tested at the WhiteSands Missile Range in New Mexico. On Monday,August 6, 1945, the nuclear bomb nicknamed “LittleBoy” was dropped on Hiroshima, Japan. On August

9,1945, Nagasaki was the target of the world’s secondatomic bomb attack. That bomb was nicknamed “FatMan.” On August 10, 1945, Japan surrendered.

What does WWII have to do with scientific notation?

Mass of a Hydrogen atom:

Proton (positive charge):0.00000000000000000000000000167 = 1.67 x 10 -27

Electron (negative charge):0.0000000000000000000000000000009109 =9.109 x 10 -31

Speed of Sound

US Navy Jet (FA-18) broke the sound barrier onJuly 7, 1999. The white halo is formed bycondensed water droplets which are thought toresult from a drop in air pressure around theaircraft.

Speed of Sound:1,126 ft. per sec. = 1.126 x 10 3 ft. per sec.

Great Wall of China

29,040,000 feet long =

2.904 x 10 7 feet long

Circumference of the Earth

24,901 miles

2.4901 x 10 4 miles

Multiplying in Scientific Notation

• Multiply the decimal numbers.• Then add the exponents of the powers of 10.• 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.

Example: Multiply (2.6 x 10 7) by (6.3 x 10 4)

• Multiply the decimal numbers.2. 6 x 6.3 =

• Add the exponents.7 + 4 =

• Put the new decimal number with the new exponent in scientific notation form.16.38 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.

• In this case, the decimal point moves one place, so add 1 to the exponent.

16.38 x 10 11 = 1.638 x 10 12

You Try!

• 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.• Then subtract the exponents of the powers of

10.• 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.

Example:Divide (1.3 x 10 11) ÷ (2.4 x 10 4)

• Divide the decimal numbers.1.23 ÷ 2.4 =

• Subtract the exponents.11 – 4 =

• Put the new decimal number with the new exponent in scientific notation form.0.5125 x 10 7

Example:Divide (1.3 x 10 11) ÷ (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.

• In this example, the decimal moves one place, so subtract 1 from the exponent.

0.5125 x 10 7 = 5.125 x 10 6

You Try!

• Simplify the following:

a. (5.76 x 10 9) ÷ (3.2 x 10 3) =

b. (3 x 10 7) ÷ (8 x 10 4) =