10.1.1 Powers of 10

Activity Symbol Activity: Powers of 10

Write each of the following numbers as a power of 10.

(a) 10,000

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(a) 10,000 equals 10 multiplication 10 multiplication 10 prefix multiplication of 10 equals 10 super four

(b) 1,000,000

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(b) 1,000,000 equals 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 prefix multiplication of 10 equals 10 super six

(c) 1,000,000,000

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(c) 1,000,000,000 equals 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 prefix multiplication of 10 equals 10 super nine

(d) What do you notice about the number of zeros in the original number and the power of 10 in parts (a) through (c)?

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(d) As you may have noticed, the number of zeros in the original number is equal to the power of 10.

Now use this idea to help you write each of the following expressions in decimal form, and as a power of 10.

(e) There are about one hundred thousand hairs on an average human head.

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(e) One hundred thousand is 100,000, or 10 super five

(f) By 2050, the population of Earth may be about 10 billion people.

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(f) Ten billion is 10,000,000,000, or 10 super 10

(g) In 1961, the French poet Raymond Queneau wrote a book called A Hundred Thousand Billion Poems.

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(g) One hundred thousand billion is 100,000,000,000,000, or 10 super 14 Queneau’s book contained ten sonnets, each with 14 lines. Each page, containing one sonnet, was cut into 14 strips with one line on each strip, so it was possible to combine lines from different sonnets to form a new sonnet. There are 10 super 14 different ways of making a sonnet in this way. So, the title of the book was correct! [ Can you explain why there were 10 super 14 different sonnets? ]

Video clip iconThis website [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] has a digital copy of the book that allows you to change lines in one sonnet.  The number of sonnets created by visitors to website already is displayed at the bottom of the page.   When we visited the site less than 1 million had been created.

Powers of 10 can be extended to write other numbers in this form. For example, 6,000,000 can be written as six multiplication 1,000,000 comma or six prefix multiplication of 10 super six. In the same way, 6,500,000 can be written as six .5 multiplication 1,000,000 or six .5 prefix multiplication of 10 super six.

When a number is written in this form, where a number between 1 and up to but not including 10 is then multiplied by an integral power of 10, it is said to be in scientific notation or standard form.

So, the scientific notation for 6,500,000 is 6.5 prefix multiplication of 10 super six, not 65 prefix multiplication of 10 super fivebecause 65 does not lie between 1 and 10. This is an important convention to remember.

10.1.2 Scientific Notation