Converting from standard form
To convert a number in standard form to an ordinary number, simply do the multiplication.
Examples
\(1.34 \times 10^3\) is 1,340, since \(1.34 \times 10 \times 10 \times 10 = 1,340\)
\(4.78 \times 10^{-3}\) is 0.00478, as \(4.78 \times 0.001 = 0.00478\)
Question
Convert the following numbers in standard form to decimals:
- \(2.99 \times 10^7\)
- \(1.36 \times 10^{-7}\)
- \(2.99 \times 10^7 = 29,900,000\)
- \(1.36 \times 10^{-7} = 0.000000136\)
Examples
\(3.51 \times 10^5\) = 351,000 because the 3 moves 5 places away from the units column. Two places are filled by 5 and 1. Put zeros in the other 3 places.
\(3.08 \times 10^{-4}\) = 0.000308 because the 3 moves 4 places away from the units column. Put zeros in the other 3 places. Focus on the 3, not the 8.
Question
What are the missing standard form measurements in the table below?
| Example | Number (metres) | Standard form |
| Height of a skyscraper | 300 | |
| Length of a virus | 0.0000003 | |
| Size of a galaxy | 300,000,000,000,000,000,000 | |
| Height of a mountain | 3,000 | |
| Nucleus of an atom | 0.00000000000003 |
| Example | Height of a skyscraper |
|---|---|
| Number (metres) | 300 |
| Standard form |
| Example | Length of a virus |
|---|---|
| Number (metres) | 0.0000003 |
| Standard form |
| Example | Size of a galaxy |
|---|---|
| Number (metres) | 300,000,000,000,000,000,000 |
| Standard form |
| Example | Height of a mountain |
|---|---|
| Number (metres) | 3,000 |
| Standard form |
| Example | Nucleus of an atom |
|---|---|
| Number (metres) | 0.00000000000003 |
| Standard form |
| Example | Number (metres) | Standard form |
| Height of a skyscraper | 300 | \(3 \times 10^2~\text{m}\) |
| Length of a virus | 0.0000003 | \(3 \times 10^{-7}~\text{m}\) |
| Size of a galaxy | 300,000,000,000,000,000,000 | \(3 \times 10^{20}~\text{m}\) |
| Height of a mountain | 3,000 | \(3 \times 10^3~\text{m}\) |
| Nucleus of an atom | 0.00000000000003 | \(3 \times 10^{-14}~\text{m}\) |
| Example | Height of a skyscraper |
|---|---|
| Number (metres) | 300 |
| Standard form | \(3 \times 10^2~\text{m}\) |
| Example | Length of a virus |
|---|---|
| Number (metres) | 0.0000003 |
| Standard form | \(3 \times 10^{-7}~\text{m}\) |
| Example | Size of a galaxy |
|---|---|
| Number (metres) | 300,000,000,000,000,000,000 |
| Standard form | \(3 \times 10^{20}~\text{m}\) |
| Example | Height of a mountain |
|---|---|
| Number (metres) | 3,000 |
| Standard form | \(3 \times 10^3~\text{m}\) |
| Example | Nucleus of an atom |
|---|---|
| Number (metres) | 0.00000000000003 |
| Standard form | \(3 \times 10^{-14}~\text{m}\) |
