Standard form is a convenient way of writing very large or very small numbers. It is used on a scientific calculator when a number is too large or too small to be displayed on the screen.

Before using standard form, we revise multiplying and dividing by powers of 10.

Calculate:

(a) | 3 × 10^{4} | |

(b) | 3.27 × 10^{3} | |

(c) | 3 ÷ 10^{2} | |

(d) | 4.32 ÷ 10^{4} |

These examples lead to the approach used for standard form, which is a reversal of the approach used in Example 1 .

In *standard form*, numbers are written as
*a* × 10^{n}
where 1 ≤ *a* < 10 and *n* is an integer.

Write the following numbers in standard form:

(a) | 5720 | |

(b) | 7.4 | |

(c) | 473 000 | |

(d) | 6 000 000 | |

(e) | 0.09 | |

(f) | 0.000621 |

Calculate:

(a) | (3 × 10^{6}) × (4 × 10^{3}) | |

(b) | (6 × 10^{7}) ÷ (5 × 10^{–2}) | |

(c) | (3 × 10^{4}) + (2 × 10^{5}) |

Your calculator will have a key
EE
or
EXP
for entering numbers in standard form.

For example, for 3.2 × 10^{7}, press

3
.
2
EXP
7

which will appear on your display like this:

3.2 ^{07}

Some calculators also display the ' × 10 ' part of the number, but not all do. You need to find out what your calculator displays. Remember, you must always write the ' × 10 ' part when you are asked to give an answer in standard form.