Approximation and Errors

Hong Kong

Stage 1 - Stage 3

Lesson

Scientific notation is a way of writing very big or very small numbers in a nice, compact way (because we all know mathematicians like to shorten everything). Funnily enough, scientific notation is frequently used in science. For example, the sun has a mass of $1.988\times10^{30}$1.988×1030kg which is much easier to write than $1988000000000000000000000000000$1988000000000000000000000000000kg.

In scientific notation, numbers are written in the form $a\times10^b$`a`×10`b`, where $a$`a` is a number between $1$1 and $10$10 and $b$`b` is any integer (positive or negative) that is expressed as an index of $10$10. If you need a refresher on how to multiply or divide by factors of 10, click here.

Remember

- A
**negative**power indicates how many times**smaller**the $a$`a`value will be. - A
**positive**power indicates how many times**larger**the $a$`a`value will be. - A
**zero**power indicates that the number will not change because $10^0=1$100=1.

What value should go in the space?

$300=\editable{}\times10^2$300=×102

Think: Let's write this expression without scientific notation.

Do:

$10^2$102 is equivalent to $10\times10$10×10 or $100$100. So we can rewrite the question as:

$300=\editable{}\times100$300=×100

So the missing value is $3$3 because $3\times100=300$3×100=300.

Given that, $\frac{1}{10}=1\times\frac{1}{10}$110=1×110$=$=$1\times10^{-1}$1×10−1, express $7\div10^{-1}$7÷10−1 in scientific notation form.

Think: How do we use this given relationship to solve this question?

Do:

$7\div10^{-1}$7÷10−1 | $=$= | $7\div\frac{1}{10}$7÷110 |

$=$= | $7\times10$7×10 | |

$=$= | $7\times10^1$7×101 |

If we round to $1$1 significant figure, sound travels at a speed of approximately $0.3$0.3 kilometres per second, while light travels at a speed of approximately $300000$300000 kilometres per second.

Express the speed of sound in kilometres per second in scientific notation.

Express the speed of light in kilometres per second in scientific notation.

How many times faster does light travel than sound?

Click here to learn more about writing values using scientific notation.