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GCSE Mathematics Syllabus Statement

Number

Subject Content:

Pupils should be taught to calculate with numbers in standard form A × 10n, where 1≤A<10 and n is an integer

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Here are some exam-style questions on this statement:

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Furthermore

Numbers in standard form, also known as scientific notation, are expressed as a×10n, where 1|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.

(3×104)+(5×103)=(3×104)+(0.5×104)=3.5×104

Subtraction:

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

(7×106)(2×105)=(7×106)(0.02×106)=6.98×106

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.

(12×103)×(4×105)=48×108

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.

=4.8×109

Division:

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

3×1096×102=0.5×107

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.

=5×106

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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