What is 10 12 4
Powers of ten with positive exponents
Powers of ten with a positive exponent are used,
to write large numbers like $$ 1 000 $$ or $$ 10 000 $$ more clearly.
The basis is always $$ 10 $$. That is always the same as the number of zeros.
$$ 1 $$ $$ = 10 $$ $$ 1 $$ thousand
$$ 1 $$ $$ = 10 $$ $$ 1 $$ million
$$ 1 $$ $$ = 10 $$ $$ 1 $$ billion
Have you noticed? Some units have prefixes that refer to the powers of ten, e.g. Megabyte.
|description||Power of ten||example|
Powers of ten are powers with:
- the base $$ 10 $$
- integer exponents
Examples: $$ 10 ^ 2 $$, $$ 10 ^ -3 $$
$$ 10 ^ n $$ means a $$ 1 $$ with $$ n $$ zeros
1) Convert to powers of ten
Task: Represent the number $$ 10 $$ $$ 000 $$ $$ 000 $$ $$ 000 $$ with a power of ten.
Step 1: Count the zeros of the number.
They are zeros.
2nd step: Use $$ 10 $$ as the base and the number of zeros as.
$$10$$ $$000$$ $$000$$ $$000=10$$
2) Calculate powers of ten
Task: Write the number $$ 10 ^ 12 $$ without a power of ten.
Step 1: Make a note of that.
The exponent is.
2nd step: Add zeros to the $$ 1 $$ according to the exponent.
$$ 1 $$ with zeros: $$ 1 $$
More positive Exponent = zeros right Add
Separate powers of ten with positive exponents
With separated powers of ten, you can make numbers like
Write $$ 200 $$ $$ 000 $$ or $$ 34 $$ $$ 000 $$ $$ 000 $$ more clearly.
separated power of ten
$$ uarr $$
$$3,4 * 10^7$$
$$ darr $$
Number between $$ 1 $$ and $$ 10 $$
$$200$$ $$000$$ $$= 2 * 10^5$$
$$34$$ $$000$$ $$000$$ $$= 3,4 * 10^7$$
The number before the power of ten is between $$ 1 $$ and $$ 10 $$, but the $$ 10 $$ is no longer allowed.
$$ a * 10 ^ z $$ $$ z $$ from $$ ZZ $$ and $$ 1≤ a <10 $$
kapiert.decan do more:
- interactive exercises
- individual classwork trainer
- Learning manager
1) Convert to separate powers of ten
Task: Write the number $$ 56030000 $$ with the power of ten separated.
Step 1: Put a after the first digit of the number.
2nd step: Count the ones after the decimal point.
The number of digits is the
the power of ten. They are digits.
So $$ 10 $$.
3rd step: Delete all trailing zeros and
multiply by the power of ten.
$$5,603 * 10$$
2) Calculate separate powers of ten
Task: Write the number $$ 2.163 * 10 ^ 4 $$ without the power of ten.
Step 1: Make a note of the power of ten.
The exponent is.
2nd step: Move the comma by the value
of the exponent to the right.
Move the comma one places to the right.
One also says: represent the number in scientific notation.
$$ 10 ^ n $$ shifts the comma by n places to the right
$$ 2.163 = 2.16300000… $$ You can add trailing zeros.
Powers with the formula editor
This is how you enter powers in kapiert.de with the formula editor (from approx. 1:30 in the video):
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