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Tiny Units in Standard Form

It is easier to read standard form than to read decimals with a lot of zeros!

Millimetres in standard form

How many millimetres are in a metre?

How much is $1 \space mm$ in metres?

Now, $1,000$ is the same as $10^{3}$ . What do you think $0.001$ is the same as?

So one millimetre is one thousandth of a metre or $0.001 \space m$

You can also write that in standard form as $1 \times 10^{-3} \space m$

$1 \space mm$ can be written as $1 \times 10^{-3} \space m$ , so how do you think you can write $2 \space mm$ ?

So $1 \space mm$ in "standard form" is $1 \times 10^{-3} \space m$

Standard form says how big the millimetre is in metres, but without all the decimals in $0.001 \space m$

Now, how about micrometres?

How do you write how many metres one micrometre is in standard form?

How big is a micrometre in metres?

A) $\frac{1}{1,000}$ of a metre B) $\frac{1}{1,000,000}$ of a metre C) $\frac{1}{1,000,000,000}$ of a metre

So one micrometre is $\frac{1}{1,000,000}$ of a metre. That is the same as ______________.

A) $0.01 \space m$ B) $0.001 \space m$ C) $0.000001 \space m$

$0.001$ is the same as $10^{-3}$ , so what is $0.000001$ the same as?

How do you write one micrometre in standard form? It begins with $1 \times ...$

A micrometre is one millionth or $\frac{1}{1,000,000}$ of a metre

So standard form for 1 micrometre is $1 \times 10^{-6} \space m$

Now, how many micrometres is $0.000005 \space m$ ?

How do you write $5 \space \mu m$ in standard form?

How many nanometres are there in a metre?

What is $\frac{1}{1,000,000,000} \space m$ as a decimal?

So 1 nanometre is the same as $0.000000001 \space m$ . How do you write that in standard form?

$0.000000001$ is the same as $10^{-9}$

So standard form for 1 nanometre is $1 \times 10^{-9} \space m$

Finally, one picometre is _______________ of a metre.

A) one millionth B) one billionth C) one trillionth

How do you write 1 picometre in standard form?

$0.000000000001$ is the same as $10^{-12}$

So standard form for 1 picometre is $1 \times 10^{-12} \space m$

What is standard form for 7 micrometres?

What is standard form for 6 picometres?

What is standard form for 9 nanometres?

Summary! You can use standard form to show how big tiny tiny units are in metres

For example, 1 millimetre is one thousandth of a metre or $0.001 \space m$ In standard form, that is $1 \times 10^{-3} \space m$

1 micrometre is one millionth of a metre

That is the same as $0.000001 \space m$ In standard form, that is $1 \times 10^{-6} \space m$

1 nanometre is one billionth of a metre

That is the same as $0.000000001 \space m$ In standard form, that is $1 \times 10^{-9} \space m$

1 picometre is one trillionth of a metre

That is the same as $0.000000000001 \space m$ In standard form, that is $1 \times 10^{-12} \space m$

Standard form means you don't have to deal with all the zeros

For example, $4 \times 10^{-12} \space m$ is a lot easier to read than $0.000000000004 \space m$ !