Succeed with maths – Part 2
Succeed with maths – Part 2

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Succeed with maths – Part 2

2 Scientific notation and large numbers

So how can you use powers of ten to write numbers in scientific notation? Let’s look at the example of six million to start with. Written in full this number is six followed by six zeroes: 6 000 000. This can also be written as: six multiplication one 000 000. Now 6 million is shown like this it can be written using a power of ten by noting that:

one 000 000 equals 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10

10 multiplied by itself 6 times is the same as 106

So, one 000 000 equals 10 super six

So, this now means that 6 million can be written as:

equation left hand side six multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 equals right hand side six multiplication 10 super six

You would therefore write 6 million using scientific notation as: six multiplication 10 super six.

Similarly, if the example had been six and a half million (6 500 000), this can be written in scientific notation as:

6.5 multiplication one 000 000 or 6.5 multiplication 10 super six in scientific notation.

So, a number written in scientific notation takes the form of: a number between 1 and 10 multiplied by a whole number power of 10. This can be shown mathematically as:

open multirelation one less than or equals number less than 10 close multiplication 10 super whole number

Thus, there are two steps to writing a number using scientific notation, as follows:

  1. Work out what the number between 1 and 10 will be.
  2. From this, decide on the power of 10 required.

So, taking the example of 130 000, the number between 1 and 10 must be 1.3, as it cannot be 0.13 or 13. 0.13 is less than 1, and 13 is greater than 1.

equation sequence 130 000 equals 1.3 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 equals 1.3 multiplication 10 super five

So, 130 000 written in scientific notation is 1.3 multiplication 10 super five. Now, it’s your turn to try some examples.

Activity 2 Understanding and writing numbers in scientific notation

Timing: Allow approximately 10 minutes

Write the following numbers without using powers of 10.

  • a.two multiplication 10 super four

Answer

  • a.equation sequence two multiplication 10 super four equals two multiplication 10 multiplication 10 multiplication 10 multiplication 10 equals 20 times 000
  • b.3.82 multiplication 10 super eight

Answer

  • b.equation sequence 3.82 multiplication 10 super eight equals 3.82 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 equals 382 000 000
  • c.9.3567 multiplication 10 squared

Answer

  • c.equation sequence 9.3567 multiplication 10 squared equals 9.3567 multiplication 10 multiplication 10 equals 935.67

Write the following numbers in scientific notation.

  • d.92 billion

Comment

1 billion is 1 followed by 9 zeroes.

Answer

  • d.92 billion equation sequence equals 92 000 000 000 equals 9.2 multiplication 10 super 10
  • e.400 trillion

Comment

1 trillion is a million million.

Answer

  • e.400 trillion equation sequence equals 400 000 000 000 000 equals four times prefix multiplication of 10 super 14
  • f.9 500 000 000 000

Answer

  • f.equation sequence nine 500 000 000 000 equals 9.5 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 equals 9.5 multiplication 10 super 12
  • g.Which of these numbers is the biggest?

Comment

Compare the powers of ten.

Answer

  • g.The highest power of the three numbers in this activity is 14, so 400 trillion is the biggest number here.

Now you’ve found out how to write large numbers using scientific notation, in the next section you’ll turn your attention back to the problem posed at the beginning of this week: how to work out the width of the observable universe in kilometres.

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