Download Standard form to Scientific

Scientific Notation
• Scientific Notation- used to express a very large or very small number. Makes numbers
easier to read.
Must be written as:
• A number that is between 1 and 10
• A power of 10 ( 𝑥 10𝑛 )
𝑎 × 10𝑛
• 𝑎 is called the Mantissa (# that is ≥ 1 and < 10)
• 𝑛 is the Characteristic (𝑛 can be any integer)
• If 𝑛 is positive the number is bigger (move decimal to the right 𝑛 times.)
• If 𝑛 is negative the number is smaller (move decimal to the left 𝑛 times.)
Standard form to Scientific
Examples: 932,000,000,000,000
and
1) Write down the numbers that are not zeroes.
932
2) Write that number as a number between 1 and 10
9.32
3) Write the number times 10.
9.32 x 10
0.00000005623
5623
5.623
5.623 x10
4) To find the exponent, count how many places you had to move the decimal.
932,000,000,000,000
0.00000005623
The exponent will be positive 14 because
you had to move the decimal 14 times to
get from 932 trillion to 9.32
The exponent will be negative 8 because you
had to move the decimal 8 times to get from
0.00000005623 to 5.623.
So the answer would be 9.32 x1014
So the answer would be 5.623 x 10−8
Scientific form to Standard
Examples: 7.1 x 1016
2.58 x 10−9
and
1) Write down the number that is being multiplied by the power of 10.
7.1
2.58
2) Move the decimal how many places the exponent is.
7.1
Positive exponent so move right
2.5
negative exponent so move left
3) Fill in the zeroes.
4) Rewrite the number.
71,000,000,000,000,000
,
.000000000258