The Operations With Standard Numbers Calculator will calculate:

- How to add, subtract, multiply and divide numbers written in the standard form.

Sum of the two numbers in standard form, S |

Difference of the two numbers in standard form, D |

Product of the two numbers in standard form, P |

Quotient of the two numbers in standard form, Q |

Sum of the two numbers in standard form Formula and Calculations |
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S = A_{1} × 10^{n1} + A_{2} × 10^{n2}S = × 10^{} + × 10^{}S = + S = S = |

Difference of the two numbers in standard form Formula and Calculations |

D = A_{1} × 10^{n1} - A_{2} × 10^{n2}D = × 10^{} - × 10^{}D = - D = D = |

Product of the two numbers in standard form Formula and Calculations |

P = (A_{1} × A_{2}) × 10^{n1 + n2}P = ( × ) × 10^{ + }P = × 10^{}P = P = |

Quotient of the two numbers in standard form Formula and Calculations |

Q = × 10A_{1}/A_{2}^{n1 - n2}Q = × 10/^{ - }Q = × 10^{}Q = Q = |

Operations With Standard Numbers Calculator Input Values |

Decimal part of the first number (A_{1}) = |

Index of the power of 10 in the first number (n_{1}) = |

Decimal part of the second number (A_{2}) |

Index of the power of 10 in the second number (n_{2}) |

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each operations with standard numbers calculation, the Operations With Standard Numbers Calculator will automatically calculate the results and update the formula elements with each element of the operations with standard numbers calculation. You can then email or print this operations with standard numbers calculation as required for later use.

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A number is expressed in the standard form if it is written as a power of ten. When a number is expressed in the standard form, it usually contains two parts: a decimal part that is a number between 1 and 10 and a part that expresses only powers of ten, as shown in the scheme below.

Y = A × 10^{n}

where 1 ≤ A < 10 and n = integer.

We can do with numbers expressed in the standard form all operations we do with ordinary numbers. However, in the addition and subtraction of numbers in standard form, there is a restriction: they must have the same power of ten, i.e. the same n. Therefore, first we do the necessary changes in any of the original numbers and after turning both of them to the same power of ten, then we can do the addition or subtraction, where only the corresponding parts A are added or subtracted, while the power of 10 does not change.

For example, if we have

3.21 × 10^{5} + 4.32 × 10^{3}

we express the second number as 0.0432 × 10^{5} and then, we add the numbers, i.e.

3.21 × 10^{5} + 0.0432 × 10^{5} = 3.2532 × 10^{5}

The general rule used in such conversions is that the number in the lowest power of 10 must fit the number that has the highest power of ten to avoid further operations in the decimal part.

Multiplication of numbers in the standard form is easier. The rule used in such an operation is "the decimal parts multiply, while indices of 10 add to each other." In symbols,

(A × 10^{m}) ∙ (B × 10^{n}) = (A ∙ B) × 10^{m + n}

For example,

(3 × 10^{5}) ∙ (5.43 × 10^{2})

= (3 ∙ 5.43) × 10^{5 + 2}

= 16.29 × 10^{7}

= 1.629 × 10^{8}

= (3 ∙ 5.43) × 10

= 16.29 × 10

= 1.629 × 10

A similar procedure is also used in the division of numbers written in the standard form. In such an operation, the decimal parts are divided while the power of ten is subtracted. In symbols,

For example,

= 2 × 10

The following Math tutorials are provided within the Powers and Roots section of our Free Math Tutorials. Each Powers and Roots tutorial includes detailed Powers and Roots formula and example of how to calculate and resolve specific Powers and Roots questions and problems. At the end of each Powers and Roots tutorial you will find Powers and Roots revision questions with a hidden answer that reveal when clicked. This allows you to learn about Powers and Roots and test your knowledge of Math by answering the revision questions on Powers and Roots.

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