# 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\$\$ \$\$=10\$\$

\$\$ 1 \$\$ \$\$ = 10 \$\$ \$\$ 1 \$\$ thousand

\$\$1\$\$ \$\$=10\$\$

\$\$1\$\$ \$\$=10\$\$

\$\$ 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.

descriptionPower of ten example
Hecto ... \$\$10^2\$\$ Hectoliters
Kilo…\$\$10^3\$\$kilometre
Mega ...\$\$10^6\$\$ megabyte
Giga ...\$\$10^9\$\$Gigaherz 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 \$\$

### Examples:

\$\$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:

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and tests
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### 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.

\$\$5\$\$\$\$6030000\$\$

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.

\$\$21630\$\$

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):