\( \DeclareMathOperator{cosec}{cosec} \)

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Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- Standard Form Test your understanding of standard form (scientific notation) with this self-marking quiz.
- Standard Form Video Learn how to write and calculate with numbers in standard form - sometimes called scientific notation.
- Standard Order Arrange the numbers given in standard form with the smallest at the top and the largest at the bottom.
- Standard Form Algebra Deeply test your understanding of standard form (scientific notation) by involving a little algebra.

Here are some exam-style questions on this statement:

- "
*(a) Write 0.0000657 in standard form.*" ... more - "
*The following table shows the distance from the sun and mass of the eight planets.*" ... more - "
*At a particular time the distance between Earth and Mercury was \(7.7 \times 10^7\) km.*" ... more - "
*A hippopotamus' heart beats approximately \(5.04 \times 10^4\) times in a day when resting.*" ... more - "
*The Moon appears to orbit around the Earth with an average radius of 385 thousand kilometres.*" ... more - "
*The volume of the Moon is \(2.2 \times 10^{10}\) km*" ... more^{3} - "
*The surface gravity, \(g\), of a planet is the gravitational acceleration experienced at its surface. The following formula can be used to find how a planet's gravity compares to Earth's.*" ... more - "
*NASA’s Transiting Exoplanet Survey Satellite (TESS) has discovered a planet between the sizes of Mars and Earth orbiting a bright, cool, nearby star. The planet, called L 98-59b, marks the smallest found by TESS yet. The radius of L 98-59b is \(5.42\times 10^6\) m.*" ... more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

If you use the TI-Nspire calculator you can find instructions for entering numbers in standard form on the GDC Essentials page.

Numbers in standard form, also known as scientific notation, are expressed as \( a \times 10^n \), where \( 1 \leq |a| < 10 \) and \( n \) is an integer. This notation is particularly useful when dealing with very large or very small numbers, as it allows for a concise representation.

When performing operations with numbers in standard form, it is crucial to follow the rules of arithmetic carefully. Here are some examples to illustrate the operations:

**Addition:**

When adding numbers in standard form, it is essential to have the same exponent. If the exponents are different, adjust them appropriately before performing the addition.

$$ (3 \times 10^4) + (5 \times 10^3) = (3 \times 10^4) + (0.5 \times 10^4) \\ = 3.5 \times 10^4 $$

**Subtraction:**

Similar to addition, when subtracting numbers in standard form, ensure that the exponents are the same before performing the subtraction.

$$ (7 \times 10^6) - (2 \times 10^5) = (7 \times 10^6) - (0.02 \times 10^6) \\ = 6.98 \times 10^6 $$

**Multiplication:**

When multiplying numbers in standard form, multiply the coefficients (the numbers in front of the power of 10) and then add the exponents of the powers of 10.

$$ (12 \times 10^3) \times (4 \times 10^5) = 48 \times 10^8 $$Remember to always express your final answer in standard form, ensuring that the coefficient is a number between 1 and 10 (including 1 but excluding 10). Adjust the power of 10 to compensate any changes you have made to the coefficient.

$$= 4.8 \times 10^9 $$**Division:**

For division, divide the coefficients and then subtract the exponent in the denominator from the exponent in the numerator.

$$\frac{{3 \times 10^9}}{{6 \times 10^2}} = 0.5 \times 10^7$$

Again remember to always express your final answer in standard form, ensuring that the coefficient is a number between 1 and 10 (including 1 but excluding 10). Adjust the power of 10 to compensate any changes you have made to the coefficient.

$$= 5 \times 10^6$$This video on Scientific Notation is from Revision Village and is aimed at students taking the IB Maths Standard level course.

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