Numbers And Units Worksheet With Answer Key (Page 7 of 8) in pdf

Numbers And Units Worksheet With Answer Key Page 7

W4-7

Appendix

Very large and very small numbers are often encountered in Chemistry. Writing them out in

full can be very time consuming and can lead to text which is difficult to read. Instead,

scientific notation (also called exponential notation) is used. Numbers are expressed in the

form:

N x 10

where N is a number between 1 and 9.9999… and n is the exponent.

Large numbers - positive exponents

Written long hand, the Avogadro constant (to 4 significant figures) is

–1

60 220 000 000 000 000 000 000 mol

In scientific notation, it becomes:

–1

6.022 × 10

mol

(read "six point zero two two times ten to the twenty-three per mole")

The exponent tells us how many times the number 6.022 is multiplied by 10 to give the long

form.

Alternatively, the exponent can be thought of as the number of times the decimal point in the

long hand form must be moved to the left in order to obtain a number between 1 and 9.9999…..

One million = 1000000.0

The decimal point must be moved 6 places to the left to give the number 1.

In scientific notation, one million is 1.0 × 10

Small numbers - negative exponents

Written long hand, the mass of a hydrogen atom is

0.000 000 000 000 000 000 000 000 001 66 kg

In scientific notation, it becomes

–27

1.66 × 10

kg (read "one point six six times ten to the minus twenty-seven kilograms")

The negative exponent tells us how many times the number 1.66 is divided by 10 to give the

long form.

Alternatively, the exponent can be thought of as the number of times the decimal point in the

long hand form must be moved to the right in order to obtain a number between 1 and 9.9999….

One millionth = 0.000001

The decimal point must be moved 6 places to the right to give the number 1.

–6

In scientific notation, one million is 1.0 × 10

Numbers And Units Worksheet With Answer Key Page 7