Multiplying and Dividing in
Scientific Notation
7th 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):
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 on
July 7, 1999. 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. = 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) =