1.1 Powers of 10
100 can be calculated by multiplying 10 by itself, that is 100 = 10 × 10 and, any number multiplied by itself can also be written using power notation. The value of the power being the number of times the number is multiplied by itself. Written in power notation, 10 × 10 is 102, said as ten to the power of two or ten squared.
Similarly, 1000 is the same as 10 × 10 × 10, or 103. This can be extended indefinitely, to give larger and larger numbers and their corresponding powers of 10.
Our first activity will give you the chance to practise writing numbers using powers of 10, before moving on to how to use these in scientific notation. If you need a hint to get going, click on Reveal comment.
Activity 1 Powers of 10
Write each of the following numbers as a power of ten.
- a.10 000
- a.Start by working out how many tens you need to multiply together, to give you 10 000, then use the knowledge that .
- b.1 000 000
- c.1 000 000 000
- d.What do you notice about the number of zeroes in the original number and the power of 10 in parts (a) to (c)?
- d.The number of zeroes in the original number is equal to the power of 10.
Use the answer to part d) to write each of the following as a number using zeroes and then as a power of 10.
- e.There are about one hundred thousand hairs on an average human head.
- e.One hundred thousand is 100 000, or 105.
- f.By 2050, the population of earth may be about 10 billion people.
- f.Ten billion is 10 000 000 000, or 1010.
- g.In 1961, the French poet Raymond Queneau wrote a book called A Hundred Thousand Billion Poems.
- g.One hundred thousand billion is 100 000 000 000 000, or 1014.
If you would like to know more about Queneau’s book, click on ‘reveal comment’.
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 1014 different ways of making a sonnet in this way.
A digital version ofallows 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 I first visited the site, fewer than one million had been created.
Now let’s look at how to use powers of ten to write large numbers using scientific notation. You’ll learn about its use with small numbers later in the week.