10.1.2 Scientific Notation

A number written in scientific notation has the following form:

Notice that to write a number in scientific notation, you can start by writing down the number between 1 and up to but not including 10. So for 130,000, this number is 1.3; then multiply this number by 10 repeatedly until you reach the number required.

Each time you multiply by 10, the power of 10 increases by 1. So, 130,000 equals one .3 prefix multiplication of 10 super five because you have to multiply 1.3 by 10 five times to get 130,000.

Activity Symbol Activity: Understanding Numbers in Scientific Notation

Write the following numbers without using powers of 10.

(a) two prefix multiplication of 10 super four

Solution Symbol

Answer

(A) two equation left hand side prefix multiplication of 10 super four equals right hand side two multiplication 10 multiplication 10 multiplication 10 multiplication 10 equals 20,000

(b) three .82 prefix multiplication of 10 super eight

Solution Symbol

Answer

(b) three .82 equation left hand side prefix multiplication of 10 super eight equals right hand side three .82 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 equals 382,000,000

(c) nine .3567 prefix multiplication of 10 super two

Solution Symbol

Answer

(c) nine .3567 equation left hand side prefix multiplication of 10 super two equals right hand side nine .3567 multiplication 10 multiplication 10 equals 935 .67

Activity Symbol Activity: Writing Numbers in Scientific Notation

Write the following numbers in scientific notation.

(a) 92 billion

Solution Symbol

Answer

(d) 92 billion equals 92,000,000,000 equals nine .2 prefix multiplication of 10 super 10

(b) 400 trillion

Hint Symbol

Comment

1 trillion is a million million.

Solution Symbol

Answer

(b) 400 trillion equals 400,000,000,000,000 equals four prefix multiplication of 10 super 14

(c) 9,500,000,000,000

Solution Symbol

Answer

(c) 9,500,000,000,000 equals nine .5 prefix multiplication of 10 super 12

Which of these numbers is the biggest?

Hint Symbol

Comment

Compare the powers of ten.

Solution Symbol

Answer

Notice how using scientific notation enables you to compare the sizes of numbers quickly. The highest power of the three numbers in this activity is 14, so 400 trillion is the biggest number here.

Video clip iconRelating to very small and very large numbers and what they mean is difficult. You may find that this website [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] which allows you to zoom out from the extremely small scale to the very large scale will start to help with this.

10.1.3 Multiplying and Dividing Numbers with the Same Base Number