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# Tiny Units in Standard Form

### 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 $0.000000000004 \space m$!