Scientific Notation

Suppose you have two numbers in scientific notation.

· Rename them so that the exponents (powers of 10) are the same,

· add the two mantissae to form the new mantissa, and append the 10 and exponent,

· if the resulting mantissa is 10 or greater then rename the mantissa and adjust the exponent accordingly.

For the first stage you may rename both numbers or either one.

For example,

3.5*10^3 + 4.5*10^4 = 3.5*10^3 + 45*10^3 = (3.5+45)*10^3 = 48.5*10^3 = 4.85*10^4

9404 in scientific notation is written as: 9.404 × 103

Then you would need lots of digits to write down some numbers, like the diameter of the known Universe in meters, the mass of the Sun in kilometers, the mass of an electron in kilograms, Avogadro's number, etc. This would be very confusing - it is much easier to have the number of digits shown in scientific notation, than having to count them every time.

The scientific notation for 57,356 is: 5.7356 × 104

0.0003458 in Scientific Notation = 3.458 x 10-4

It is scientific notation if it is written in the form

a*10b where 1 ≤ |a| < 10 and b is an integer.

The vertical bars around a indicate its modulus: that is, the non-negative value of a.

Ketchup

6.0 × 10-1

1987

Wherever numbers get very big or very small.

310233 = 3.10233 x 105. The decimal place was moved 5 places to the left to make the mantissa between greater than or equal to 1 and less than 10. The exponent is positive if the original number is bigger than 10.

3.17 x 104

4.2*10^1

300 in Scientific Notation = 3 x 102

1.15 x 101

2.3*107

Hypothetical question for you here:

Would you rather write

54,000,000,000,000,000,000,000,000

or

5.4 x 10^25

It's much faster to write, plus you don't have to count zeroes. It's an easy way to write really, really small numbers, or really, really large numbers.

0.0008549 = 8.549 × 10-4

8762 = 8.762 x 1000 = 8.762 x 103

6.25 million in Scientific Notation = 6.25 x 106

To convert a number to scientific notation: · If the number has no decimal point, then add one at the end. · Then move the decimal point to just after the first digit while counting the number of places you have moved it. · The mantissa of the new number, formed after moving the decimal point is a. · If the original number is negative, then so is a. · The number of places to the left that the decimal point was moved is b. If it was moved to the right, then b is negative. For example: 23045.06 becomes 2.304506*10^4 -23045.06 becomes -2.304506*10^4 0.00023004 becomes 2.3004*10^-4

1.25 X 102 is the real question srry

It is 5.620*10^0 or, more simply, 5.620

It is: 2.5*10^13 miles